President Obama and Chinese President Xi Jinping walk at the Sunnylands estate June 8, 2013, in Rancho Mirage, Calif. (Evan Vucci/AP)

When Chinese President Xi Jinping arrives in Washington next week, President Obama plans to welcome him with a 21-gun salute on the South Lawn and a black-tie state dinner, the highest level of diplomatic pageantry for a foreign leader.

But some in Washington are calling on Obama to keep the cork in the champagne.

The mood toward China on Capitol Hill has soured after a year in which the Chinese are suspected in the cybertheft of millions of U.S. government personnel records and China’s navy has ignored warnings over the construction of military outposts in the South China Sea. Recent turmoil in China’s economy was a final straw: Lawmakers in both parties want a tougher U.S. policy.

“We should not roll out the red carpet for him,” said Sen. Marco Rubio (Fla.), one of several Republican presidential candidates who say Obama should cancel or downgrade Xi’s visit.

West Wing advisers called such a move unthinkable at a time when the White House is counting on Beijing’s commitment to a major agreement to slash greenhouse-gas emissions by 2030 and its backing of the U.S.-led nuclear accord with Iran.

Chinese President Xi Jinping accompanies President Obama to view an honor guard during a welcoming ceremony inside the Great Hall of the People on Nov. 12, 2014, in Beijing. (Feng Li/Getty Images)

“The debate over protocol is a bit of a cul-de-sac because the Chinese are a major power,” said Ben Rhodes, a deputy national security adviser. “When U.S. leaders met with Soviet leaders, there was pageantry just because they were two very powerful countries.”

The sensitivities around how the summit is handled has been on display in recent days, as the White House privately debated whether to enact economic sanctions on Chinese businesses that have benefited from the cybertheft of U.S. trade secrets.

Such an unprecedented move would have risked embarrassing and provoking Xi. Instead, administration officials decided to hold off after meeting with a high-level Xi aide last week in Washington.

In an interview before that decision was reached, Rhodes acknowledged that Xi has been a more assertive leader than the administration expected. In a blunt showing of China’s growing ambitions, Chinese navy ships transited U.S. territorial waters near Alaska while Obama was visiting the state.

But Rhodes emphasized that China also has offered crucial support on several of the United States’ global priorities. And he said it would be beneficial for Xi, who will meet business leaders in Seattle and talk with lawmakers on Capitol Hill, to hear directly from aggrieved parties.

“The question is whether we can channel that assertive behavior in directions that are consistent with our interests,” Rhodes said. “If we limit our ability to interact or scale back the visit, all that might succeed in doing is making us feel good. It will not advance our interests.”

For decades, Washington and Beijing have engaged in a wary courtship; they are nations that are at once global partners and strategic rivals. As China’s international clout has grown, the United States has sought to support its peaceful rise, deepen economic ties and coax the Asian power into more responsible global citizenship.

President Obama and Chinese President Xi Jinping attend a news conference at the Great Hall of the People on Nov. 12, 2014, in Beijing. (Feng Li/Getty Images)

But time and again, the countries’ ability to work together has been tested by their clashing values and deep mutual suspicions.

China’s unique standing is evident in that it is the only non-democracy among the eight nations whose leaders have been granted an official state visit by Obama. (Then-President Hu Jintao also feted in 2011.)

Foreign-policy analysts described the Chinese as protocol-obsessed and said Xi would be unwilling to travel to Washington without the full menu of ceremonial flourishes. But they also cautioned that the Chinese largely view the get-togethers as elaborate photo ops, meant to present a picture of equal powers on the world stage.

David Shambaugh, a foreign-affairs professor at George Washington University, said Chinese officials don’t care about the issues. “They want the photo ops for their own domestic audience — 21 guns, nice silverware,” he said. “That’s what it’s all about, so when they get back home they can tell their people, ‘The Americans received us at the highest level we are due.’ ”

Obama aides scoffed at what one called “outdated thinking,” and they pointed to the climate deal announced last year in Beijing. But for all of the pomp at the summits, both sides engage in passive-aggressive ma­nipu­la­tion aimed at exerting control and sending symbolic messages.

When President Bill Clinton made his first visit to Beijing in 1998, his hosts informed the White House that the arrival ceremony would take place next to Tiananmen Square.

Clinton aides balked. The president had inveighed against the “butchers of Beijing,” and his advisers wanted him nowhere near the site where the Communist Party had crushed democratic uprisings in 1989.

“We did not want to be seen as whitewashing Tiananmen,” recalled Jeffrey Bader, a China expert on Clinton’s staff who also served in the Obama administration. “We thought the American press would seize on it.”

After weeks of wrangling, the Chinese prevailed. But Clinton got a measure of payback at a news conference when he engaged Chinese President Jiang Zemin in a long and pointed debate about human rights.

In 2006, President George W. Bush, wary of giving the Chinese a full diplomatic embrace, downgraded Hu’s visit by treating him to a luncheon instead of a dinner.

More embarrassing to the Chinese was the bungled welcome ceremony on the South Lawn. The U.S. announcer called for the anthem of the “Republic of China” — which is the official name of Taiwan. Then an anti-Communist Party activist from the meditation movement Falun Gong, who had entered with a news-media credential, interrupted Hu’s remarks by shouting threats until she was removed by the Secret Service.

“One of the most important issues for the Chinese when they come is the Falun Gong,” said Joseph Hagin, who served as Bush’s deputy chief of staff for operations. “They even want them kept away from being visible in their motorcades. We say: ‘Look, the president drives by demonstrations all the time. It’s a free country. There’s only so much we can do.’ ”

The Chinese exert more control on their own turf.

In November 2009, Obama visited Hu in Beijing, eager to project a new era of U.S. engagement abroad. But at every turn, Hu appeared determined to thwart the American president.

At a town-hall-style meeting in Shanghai, Chinese officials refused White House requests to stream Obama’s remarks live online. The hosts further undermined the event by planting milquetoast questions with a pre-screened audience.

At the post-summit news conference, Hu embarrassed the U.S. delegation again by refusing to let reporters ask questions. Hu’s heavy-handed stage management earned Obama headlines about his naivete.

“The Chinese always like a Potemkin press conference with no questions asked,” said Orville Schell, a China expert at the Asia Society. “The challenge for the U.S. is to make it as open as possible.”

The Obama administration has sought to increase face-to-face meetings with the Chinese at all levels of government, in hopes of avoiding military mishaps or other confrontations. Rhodes said U.S. allies and partners in Asia, who are wary of China’s rising influence, “do not want to see us isolate and embarrass the Chinese. They want to see us engaging them.”

Among the strategies the Obama White House has adopted, aides said, is to push the Chinese outside their comfort zone to spur more unscripted exchanges.

In 2013, Obama invited Xi, who had recently assumed power, to the Sunnylands estate in Southern California for a more informal summit to break the ice. Thomas E. Donilon, then Obama’s national security adviser, traveled to Beijing to negotiate the agenda with Chinese officials, including Xi, who showed up at the Great Hall of the People with a pen and legal pad to take notes.

The Americans, hoping the relaxed setting would build trust, arranged for the two leaders to take a one-hour stroll around the campus, unaccompanied by aides. In a dinner toast, Xi surprised Obama with a bottle of Maotai liquor, the same spirit poured for President Richard M. Nixon on his historic visit to Beijing 40 years earlier.

Behind the show of camaraderie, though, Xi was more circumspect: His traveling party refused to stay in the estate’s guest rooms, fearing they had been bugged by the Americans.

The results of the summit have been disappointing. One session was devoted to U.S. concerns over China’s cyberespionage on American businesses, a situation that has grown only worse.

“The Chinese side can’t expect they can just come to the United States, have a gracious welcoming by the president, get all the protocol right and think that’s a successful summit,” Donilon said in a recent interview.

White House aides point to breakthroughs. Last fall, during Obama’s visit to Beijing, the two sides presented a united front during a news conference to announce the climate deal on greenhouse gases. But their clashing worldviews were on display again when an American reporter challenged Xi over China’s policy of denying visas to foreign correspondents because of critical coverage.

Visibly irritated, Xi declared that the foreign media should “obey China’s laws” and look at themselves “to see where the problem lies.” He also denounced pro-democracy protests in Hong Kong as an “illegal movement” and suggested that the United States butt out of China’s domestic affairs.

It was a jarring moment, but one that revealed more than the gauzy dinner toasts and photo ops.

“It showed we have a different view of these issues,” Rhodes said. “It was a window into the complexity of the relationship.”