The Senate passed, 52-48, a resolution Wednesday to nullify an Occupational Safety and Health Administration rule requiring employers with 100 workers or more to require COVID-19 vaccinations or weekly tests for employees.

But the resolution faces a more uncertain future in the House, where House Republicans would have to secure support from five Democrats to force a vote. Most Democrats back the administration’s policy to require shots or tests, saying the policy protects the public from the virus.

Two Senate Democrats, Joe Manchin III of West Virginia and Jon Tester of Montana, voted for the resolution, which was offered by Republicans last month.

Republican senators say the mandate is a top concern of constituents. They warn that the mandate could lead to people losing their jobs and note that courts have stayed the policy for now.

“The anxiety of people in my state of West Virginia and I’m sure all of our states over this vaccine mandate is real,” Sen. Shelley Moore Capito, R-W.Va., said at a press conference Wednesday. “I think they realize that this is an invasion into their own abilities to make decisions about themselves and their health care.”

Sen. Mike Braun, R-Ind., who sponsored the resolution, argued “hardly any transmission is occurring at the business level, or what you do during the day,” and said the requirement is an example of government overreach.

“That is the heavy hand of government,” Braun said.

Republicans also say they support vaccination, just not mandates, and many urged people to get a booster shot as the new omicron variant threatens to become the dominant strain of the virus in the United States.

“I want to emphasize how important the vaccine is, and especially booster shots,” said Sen. Roger Marshall, R-Kan. “With omicron variant, without the booster shot, you’re probably not going to be protected much at all.”

Republicans also plan to introduce another Congressional Review Act resolution to target a separate Centers for Medicare and Medicaid Services rule requiring most health care workers to be vaccinated, Marshall said.

Senate Majority Leader Charles E. Schumer, D-N.Y., said at a press conference this week that reversing the rule could speed up the spread of dangerous new variants.

“It’s an important moment for the federal government and national leaders to double and triple down on encouraging all eligible Americans to get vaccinated and boosted as soon as possible,” he said Tuesday. “This week, Republicans want to take us in the opposite direction with an anti-science, anti-vaccine vote that not only divides our country but hurts our ability to fight COVID.”

Republicans in the House also hope to force a vote on the resolution, although the earliest they could do so under the chamber’s rules would likely be in late January, since lawmakers could file a discharge petition 30 legislative days after the resolution’s introduction if 218 members co-sponsor it.

While all House Republicans support the resolution, they would need five Democrats to sign on to the measure to bring up a discharge petition.

White House Press Secretary Jen Psaki said this week that President Joe Biden would veto the resolution if Congress clears it.

Rep. Fred Keller, R-Pa., who leads the House effort, said he hoped the Senate vote would help to convince some Democrats in that chamber to sign on as a co-sponsor.

“We’re certainly going to see it come out of the Senate, and that’s going to be part of what we use to discuss the fact that it does have bipartisan support in the Senate and that the Senate is standing up for the rights of the people,” Keller said in an interview. “I’m not really leaving any stone unturned. I think that the entire Democrat conference should be engaged in this.”