Former Republican National Committee Chair Michael Steele condemned the GOP effort, calling it an "act of cowardice."
Senators Amy Klobuchar and Bill Cassidy joined U.S. health officials on Sunday to push booster shots as more countries reported their first cases of the Omicron variant.
More than a dozen other GOP lawmakers recently signed a letter supporting a demand that President Joe Biden undergo such a test.
"Wacky Senator Bill Cassidy from Louisiana is a RINO Republican who begged for my endorsement in 2020," Trump said.
Sen. Bill Cassidy was one of seven Republican senators who voted to convict Donald Trump during his second impeachment.
"Elections are about winning," the Louisiana Republican said.
"If we relitigate 2020 over and over again, it won't change the result in 2020, but we are sure to lose in 2024," said the Louisiana Republican.
"This isn't just about hospitals and nursing homes," Graves, a Louisiana Republican, said. "Electricity is literally the difference between life and death."
The high court's Wednesday ruling "was only on if the plaintiffs had standing," the Louisiana Republican said Sunday.
"What ISIS-K has done has already stopped the flow of folks who need to get out," the Louisiana Republican said.
"I do disagree with Governor DeSantis. The local official should have control here," the Republican senator said Sunday.
"I just don't know how you have a cloture vote when you don't have a bill ready," said Senator Bill Cassidy on Sunday.
The senator from Louisiana said "it shouldn't be the president advocating" for the vaccine, but rather the healthcare workers in the state.
Ocasio-Cortez responded to Cassidy's earlier statement that physical infrastructure, such as bridges and roads, could be an issue for women because they are often the ones "taking the children to school" or "doing the shopping."
Republican support for the Bipartisan Infrastructure Framework appears to be in jeopardy as criticism has mounted.
"Unfortunately, over the last four years we had a track record of losing," Sen. Bill Cassidy (R-La.) said Wednesday while speaking about former President Donald Trump's time in the White House. "We need to win going forward."
"What's wrong with raising the top tax rate to where it was during the Bush and Obama administrations in order to help the working and middle class?" Chris Wallace asked the Republican lawmaker.
"Senator, are you saying the people of your state don't need that money?" Chris Wallace asked.
"You can't help but notice that the administration changes, and there's a surge," the Louisiana senator said.
The Republican lawmaker discussed the state of the GOP following Trump's presidency during an appearance on CNN's 'State of the Union' Sunday morning.
The Louisiana Republican told reporters he was "at peace" with the decision, despite the censure from his state party.
Some of the Republican senators who voted to convict former President Donald Trump at his impeachment trial faced censure from local GOP groups in their states.
Susan Collins of Maine said Trump created a "dangerous situation" and put his "selfish interest" over the interests of the country.
Cassidy, alongside six fellow Republican senators, voted to convict the former president of inciting last month's insurrection at the U.S. Capitol.
Some Republicans are calling for the GOP senator, who doesn't plan to run in 2022, to be formally censured.
"We condemn, in the strongest possible terms, the vote today by Senator Cassidy to convict former President Trump," the LAGOP said in a Saturday tweet.
The Maine Republican senator said the former president had subordinated "the interests of the country to his own selfish interests."
The Republican senator said he wasn't "leaning one way or the other" on Trump's impeachment.
Six Republican senators joined Democrats and affirmed that it was permissible to try a former president.
Senator Lindsey Graham spoke to Trump on Tuesday night and reminded him that 44 senators voted to dismiss the case.