The legislation would rename a part of the street across from China's embassy after a pro-democracy activist jailed by Beijing. It would effectively change the embassy's address to "1 Liu Xiaobo Plaza," after the Nobel Peace Prize winner serving an 11-year sentence in part for publishing an anti-Communist manifesto calling for political freedoms.
China's Foreign Ministry blasted Cruz's bill as a "political farce" and warned that it would have serious repercussions for its relationship with the U.S if it were to pass the House and become law. The measure cleared the Senate in a unanimous voice vote on Friday.
Victoria Coates, Cruz's national security advisor, told CNN that the candidate understands the U.S. has strong ties to China and that he doesn't want to be "overtly antagonistic."
But she said Cruz feels that human rights have been ignored "since the beginning of the Obama administration, since Secretary (of State Hillary) Clinton went to Beijing in February 2009 and said we were going to have a separate track for human rights. The Chinese said they interpreted that as human rights on the back burner."
The tiff comes as President Barack Obama meets in California with Southeast Asian leaders, in part to discuss increasingly assertive Chinese moves in the South China Sea and reassure China's neighbors that the U.S. is committed to protecting their interests in the region.
"If the relevant bill is passed into law, it will cause serious consequences," Chinese Foreign Ministry spokesman Hong Lei said in a statement, which also called Cruz's bill "contrary to the basic norms" of international relations.
"We demand the U.S. Senate stop promoting the bill and hope the U.S. executive authorities put an end to this political farce," the spokesman said.
A White House official, speaking anonymously to discuss sensitive issues, dismissed Cruz's bill as a "stunt."
"While we continue to impress upon China the imperative of respecting human rights and releasing Liu Xiaobo, as well as other political prisoners, we do not believe Sen. Cruz's ploy to rename a street in Washington, D.C., is an effective way to achieve either goal," the official said. "In fact, legislative stunts such as this complicate our efforts."
The administration has indicated that President Barack Obama would veto the bill if it reached his desk, with the White House official saying, "We oppose this approach and would prefer to work with Congress on more productive ways to address our shared goal of improving human rights in China and around the world."
Cruz hit back, saying in a statement that "the Obama administration's veto threat is yet another outrageous example of its eagerness to coddle an authoritarian Communist regime at the expense of pro-American dissidents."
"The moral high ground enjoyed by the United States is an advantage when dealing with a country like China, not something to be voluntarily abandoned," Cruz continued. "How ironic it is that the 2009 Nobel Peace Prize laureate is threatening to veto a bill honoring the 2010 one."
It's not the first time in this presidential campaign that a candidate has used China in an attempt to demonstrate tough foreign policy chops. GOP front-runner Donald Trump has repeatedly said that he would have China declared a currency manipulator on his first day in office.
That idea is supported by U.S. manufacturers who argue that China keeps its currency artificially low to make its exports cheaper, but Obama, like predecessor George W. Bush, has preferred to use international pressure and diplomacy to try to move China.
In September, a Chinese Foreign Ministry spokeswoman dismissed Trump's pledge as a mere "disturbance" that wasn't to be taken seriously as an official U.S. government position.
Cruz has been using campaign appearances to stress that he would pursue a muscular foreign policy without concern for what he on Tuesday labeled a culture of political correctness at the Pentagon.
In Mount Pleasant, South Carolina, he told troops that their ready-to-eat rations would never be gluten-free and that under his leadership, the military would be "feared by our enemies and trusted by our allies."
The Texas Republican has often used China as a foil. He introduced a resolution to rename the street across from China's embassy in a leafy northwest Washington neighborhood in September and then again in October.
The sprawling Chinese embassy compound was designed by I.M. Pei and opened in 2009, one of more than a dozen diplomatic missions located in upper Washington.
Both times, Cruz's effort was blocked by Sen. Dianne Feinstein, a California Democratic, who objected that Cruz had given his colleagues only one hour's notice before introducing the resolution.
"Maybe people don't believe diplomacy makes a difference, but I do," Feinstein said at the time. "I think there will be ample time for the President to speak with the President of China and for some of us to speak as well."
Undeterred, Cruz introduced his bill on February 12.
The Senate cleared the bill later that day at the same time that Cruz lifted a hold he had long placed on a slew of diplomatic nominations -- including ambassadors to Norway and Sweden and the State Department's under secretary for political affairs -- to protest of the Iran nuclear deal.
National-level politicians have gotten interested in this local Washington street before. In 2014, a bi-partisan group of lawmakers, including Hose Minority Leader Nancy Pelosi, asked Washington's mayor to rename the street after Liu Xiaobo to coincide with the 25th anniversary of the Tiananmen Square killings.
Since the street is actually federal property, Virginia Republican Rep. Frank Wolf also put an amendment in the 2015 State Department spending bill that required Secretary of State John Kerry to change the street name. The House appropriations committee approved the amendment, but it was later dropped.
There is also precedent for such a move. In 1984, the year Soviet athletes boycotted the summer Olympics in Los Angeles, California, and a year after then-President Ronald Reagan declared the Soviet Union an "evil empire," the Senate passed a measure changing the official address of the USSR's embassy on Washington's 16th Street to No. 1 Andrei Sakharov Plaza, in honor of the anti-Soviet dissident and Nobel laureate.
The Senate took the step after Sakharov went on a hunger strike in 1984 after the government prohibited his wife from traveling abroad for medical treatment.