Cassidy, Graham, Johnson and McCain on Thursday vowed not to vote in favor of a so-called "skinny" Obamacare repeal unless Republican leadership in the Senate assures them the bill will go to a conference committee.
"I am not going to vote for a piece of legislation that I believe is not a replacement," Graham told reporters in a press conference. "The 'skinny' bill doesn't work for any state."
"Obamacare is collapsing and the 'skinny' bill won't prevent it from collapsing," the 2016 GOP presidential candidate added.
"As for the 'skinny' bill being a replacement for Obamacare ... that's about as accurate as [Former] President [Barack] Obama telling you if you like your doctor you can keep your doctor."
Johnson echoed Graham's remarks, arguing that a 'skinny' repeal of Obamacare would not fulfill the longstanding Republican promise to entirely scrap the controversial healthcare law.
"I'm sorry, the skinny bill in the Senate doesn't even come close to our promise to repeal Obamacare," he said. "Just give us the assurance that whatever we pass tonight will go to conference."
McCain, who was diagnosed earlier this month with brain cancer, added that he hopes Republicans and Democrats collaborate on meaningful healthcare reform.
"We've got to see some bipartisanship," he said. "Obamacare is a failure. It needs to be fixed. It's time we sat down together and came up with solutions that work for the American people."
Republican leaders have not unveiled the details of their "skinny" repeal plan, but it is expected that it would repeal Obamacare's employer and individual mandates.
Senate Majority Leader Mitch McConnell (R-Ky.) can only afford two Republican senators defecting on the bill, assuming all Democrats oppose it and Vice President Mike Pence then breaks a tie after 50 votes in favor of it.
If the Senate ultimately passes the legislation, both chambers of Congress would then have to approve whatever emerges from their conference together.
Republicans have struggled to decide the best strategy for repealing Obamacare, with conservatives and moderates disagreeing over parts of the process.
President Trump has made repealing and replacing Obamacare a key priority of his presidency, having campaigning extensively on that promise in 2016.
Republican Sens. John McCain (AZ), Lindsey Graham (SC), Ron Johnson (WI) and Bill Cassidy (LA) on Thursday held a press conference to discuss the so-called "skinny" Obamacare repeal bill under consideration in the Senate.