That’s provided an opening for both Treasury Secretary Janet Yellen and Commerce Secretary Gina Raimondo to become the lead envoy. Both have said they wanted to travel to China, and, unlike Blinken, both have received public invitations from Chinese cabinet agencies. Treasury and Commerce have dispatched officials to Beijing to scout out possible meetings, although neither session is far along in planning. Yellen had expected to go to China in March until the balloon incident put the kibosh on that visit.

The bureaucratic wrangling has been fairly civil thus far by Washington standards, but the Biden administration is eager to tamp down any notion of internal conflict.

“The Administration has been clear about maintaining channels of communication with Beijing to manage competition responsibly,” said National Security Adviser Jake Sullivan in a statement. “The engagements Secretary Blinken, Secretary Yellen, Secretary Raimondo and others will have in the coming months will all be a part of that.”

It’s also not as simple as who the U.S. may want to send. Chinese officials are also jostling over who should meet an American emissary, and it’s uncertain whether any of the Americans could score a meeting with Chinese leader Xi Jinping. Meanwhile, as friction grows between the two superpowers, some wonder if détente is even possible at this point.

“We have left strategic competition behind,” said Christopher K. Johnson, a former CIA China analyst. “We’re in strategic rivalry and are at the risk of careening toward strategic enmity.”

Last November, the two sides looked as if they wanted an accommodation. Biden and Xi met in Bali and, despite their many differences, agreed that the two sides should work together on economic stability, food security, climate and other issues.

But follow-up meetings were scrapped after the balloon saga embarrassed Beijing. Then, China launched military drills around Taiwan after the island’s leader met with Speaker Kevin McCarthy in early April, which outraged Washington.

Since March, the Chinese have sent conflicting signals about their interest in warming ties with the U.S. On the one hand, Chinese leaders have used mainland economic conferences to welcome U.S. business investment. On the other, Beijing has raided an American financial analysis firm in Beijing and slowed merger approvals needed by American companies. Xi accused the U.S. by name — a breach of Chinese etiquette — of “all-round containment, encirclement and suppression.”

There are two strands of thought among the Chinese leadership, said Harvard University’s Graham Allison, a prominent political scientist who recently met with top Chinese leaders in Beijing. “One strand is fatalistic,” he said. “The second strand says, ‘We can’t let things remain this way. We need to get back to Bali, with private conversations about the flashpoints that matter most.’”

The U.S. has tried to pick up on that second strand but hasn’t gotten very far. Meetings of U.S. and Chinese officials are “like being trapped in a bad episode of ‘Seinfeld’ where the ‘Festivus airing of grievances’ is a year-round holiday,” said Johnson, who now heads the political-risk consultancy China Strategies Group.

Administration officials acknowledge Blinken hasn’t had much luck changing that dynamic, but they argue China’s top foreign affairs official, Wang Yi, and others are at least as much at fault for the downward spiral. The Financial Times also recently reported that Chinese officials are worried that the FBI would release a report on the balloon incident if Blinken visited Beijing, once again embarrassing them. Still, the bad vibes have the White House weighing the pros and cons of various potential envoys.

So far, Yellen hasn’t been at the center of China policymaking. The National Security Council plays an outsized role there, with the State Department also having an important voice. But issues fundamental to Treasury — global economic growth, financial sector stability — are among those China wants to discuss with the U.S. even as the two countries tangle over Taiwan, Russia and technology.

There’s also precedent for Yellen taking a lead on China. In the past, Treasury secretaries have played important roles as China envoys. In 1999, the U.S. mistakenly bombed China’s embassy in Belgrade during the Kosovo War, igniting protests across China. President Bill Clinton dispatched Treasury Secretary Larry Summers to meet China’s premier in the dusty city of Lanzhou in western China. Summers carried a letter from Clinton pledging to help China join the World Trade Organization. The tactic worked and the two sides soon started negotiating again.

Nine years later, Treasury Secretary Hank Paulson, who had long been friends with Chinese leaders, helped convince Beijing to work closely with President George W. Bush in fighting the global financial crisis. China’s economic officials in turn pressed Paulson to protect China’s stash of $1 trillion in U.S. government debt.

But Summers and Paulson were close to the White House and had something China wanted from the U.S. — WTO membership in Summers’ case, cash preservation in Paulson’s. Yellen has neither advantage. In many parts of the administration, the former Fed chair is still seen as academic and politically naive. Notably, she publicly criticized the heavy tariffs on Chinese goods imposed by the Trump administration, which Biden so far has decided to keep.

“She is afflicted with honesty,” said Ryan Hass, an Obama White House China expert now at the Brookings Institution.

Treasury is also viewed elsewhere in the government as holding on to the idea that a formal economic “dialogue” between the two nations would be useful, although the Biden White House has picked up Trump’s position that the Chinese used earlier dialogues, where senior officials met regularly, to filibuster a subject. Some at Treasury make sure not even to use the word “dialogue” when asking for White House approval to call or meet with Chinese counterparts.

“Yellen has been somewhat dovelike,” said a senior Biden foreign policy official. “On a number of key issues, she and the president aren’t on the same page. That will play a role where this ends up.”

During a speech last week at the Johns Hopkins School of Advanced International Studies, Yellen gave a tough-minded preview of the kinds of conversations she anticipated having with the Chinese. The speech had two audiences: Beijing and those in Washington and the allied capitals that doubted the White House fully trusted her.

National security is of “paramount importance,” she said, with the U.S. focusing on keeping leading-edge technology from reaching the Chinese military and security establishment. But she tried to assure her Chinese listeners that the U.S. doesn’t want to decouple entirely from the Chinese economy, which, she said, “would be disastrous for both countries.”

“These national security actions are not designed for us to gain a competitive economic advantage, or stifle China’s economic and technological modernization,” Yellen said.

In other words, the two nations would disagree on many fronts, but there were still plenty of areas where they could profitably work together.

Within the White House, no decision has been made on whether Blinken, Yellen or Raimondo will be the initial envoy to Beijing. One consideration: Which of them would wrangle a meeting with the highest-ranking Chinese official?

That makes Raimondo a long shot for the first trip to Beijing. Commerce secretaries traditionally rank low in the Washington hierarchy and have been generally treated in Beijing as salespeople for corporate America. However, Raimondo plays a critical role in sanctioning Chinese companies and overseeing U.S. industrial policy — areas the Chinese want to discuss. Vice Premier Ding Xuexiang, one of the seven members of the ruling Politburo Standing Committee, is expected to oversee technology issues for Beijing and would be a high-profile interlocutor on the Chinese side.

The State Department argues that Blinken should go first because State has a wider portfolio of issues than Treasury, including Taiwan, Russia’s war against Ukraine, military cooperation, fentanyl exports, imprisoned Americans and climate talks.

Some at State also are concerned that the Chinese could look to splinter the U.S. government by favoring Treasury and trying to cut out the State Department. In the Trump administration, for instance, the Chinese focused their lobbying on Treasury Secretary Steven Mnuchin to try to sideline the uber-hawkish U.S. Trade Representative Robert Lighthizer, who was pressing a trade war between the two nations.

It didn’t work under Trump, and U.S. officials say it wouldn’t work now. Beijing “won’t find a way to divide what we’re doing,” said Deputy Treasury Secretary Wally Adeyemo. “What we are trying to do is make it clear that we are going to protect our national security, but our goal is not to constrain China’s economy from growing.”

Before the balloon incident, Blinken intended to fly to Beijing to discuss a range of issues with his Chinese counterparts, including macroeconomic issues — but no “dialogues” — and expected to get a meeting with Xi Jinping. Treasury secretaries rarely meet with the top leader in one-on-one sessions. Instead, they often get time with China’s premier, the number two official who is usually in charge of running the economy. At the very least, Yellen would expect to meet with He Lifeng, China’s new vice premier in charge of trade and macroeconomics. In his previous job, He oversaw domestic economic planning and didn’t meet much with U.S. officials.

For all the aggravation with Blinken in Beijing, China’s Ministry of Foreign Affairs also has been throwing up some roadblocks to an early Yellen visit, said several China experts who have recently visited Beijing. Presumably, that’s for reasons similar to those in Washington; each ministry wants to assert its preeminence and have its ministers host the first U.S. cabinet visit since the balloon imbroglio. That’s especially important now in Beijing where Xi has reshuffled top government and Communist Party officials.

“There is a little bit of staking out one’s turf,” said former Clinton trade representative Charlene Barshefsky, who closely tracks Chinese politics. “There is a new set of ministers. They are letting it be known their jurisdiction and their predilections for policy.”

A spokesperson for the Chinese embassy said in a statement that the U.S. “should follow through on the common understandings between the two heads of state in Bali, so as to create the conditions and atmosphere needed for high-level exchanges and bring China-U.S. relations back to the right track.”

In the end, whom Biden chooses to make the first cabinet-level trip to Beijing may come down to who is available to travel when preparations are completed. The U.S. envoy may carry a letter from Biden during the trip. An important goal of this round of diplomacy is promoting a summit between Biden and Xi in November in San Francisco when the U.S. hosts the Asia-Pacific Economic Cooperation forum, an organization of 21 major economies, including the U.S., Japan, China and Russia.

But it’s far from clear that cabinet-level meetings will be enough for China to start modulating its policies. The U.S. has plenty it could offer China as inducements — cuts to tariffs that even Biden criticized when he was running for president in 2020, limiting U.S. export controls, backing away from banning TikTok in the U.S., among many other possibilities.

“At this moment, we need deeds as well as words,” said Summers, the former Treasury secretary.

But across the government, U.S. officials say the focus now is on restarting talks, not about making changes in policy — particularly anything resembling a concession that could be criticized by Republicans.

“We want senior empowered channels of communication,” said a senior State Department official. “We want to engage regularly.”

For Washington, in other words, the meetings are the message.