Senate Majority Whip John Cornyn John CornynTumultuous court battle upends fight for Senate Texas Democrats roll out first wave of planned digital ads as Election Day nears Calls grow for Biden to expand election map in final sprint MORE (R-Texas) on Tuesday said Congress should move onto tax reform and not try to pair it with a new plan to repeal ObamaCare.

Cornyn signaled the widespread GOP fear that adding a health-care debate to the tax bill will only bog down a reform package that is President Trump’s new top priority.

Cornyn, the No. 2 Republican in the Senate, said he does not support combining tax reform and ObamaCare repeal in a single budget reconciliation measure that would allow the GOP to protect their bill from a Democratic filibuster.

ADVERTISEMENT

Separately, the chairman of the House Freedom Caucus also said he opposed the idea, saying it could "interfere potentially with tax reform."

"Since we have fumbled at least twice now on health care, to include it and make tax reform contingent on us getting across the finish line on health care, I wouldn't be in favor unless we can keep it on parallel tracks," Chairman Mark Meadows (R-N.C.) said.

Sen. Lindsey Graham Lindsey Olin GrahamGraham: GOP will confirm Trump's Supreme Court nominee before the election Fox's Napolitano: Supreme Court confirmation hearings will be 'World War III of political battles' Grassley, Ernst pledge to 'evaluate' Trump's Supreme Court nominee MORE (S.C.) and other Republicans have floated the combined package as a way for the GOP to keep its dream of ObamaCare repeal alive.

Legislation introduced by Graham and Sen. Bill Cassidy William (Bill) Morgan CassidyCoushatta tribe begins long road to recovery after Hurricane Laura Senators offer disaster tax relief bill Bottom line MORE (R-La.) does not have the support to pass the Senate, and existing budget rules that prevent Democrats from filibustering the GOP’s ObamaCare repeal bill expire on Sept. 30.

“I think the work should continue,” Cornyn said of the health-care bill. “Sen. Cassidy and Sen. Graham have come up with a good idea but one that we haven’t had time to socialize yet.”

He noted that Senate Health, Education, Labor and Pensions Committee Chairman Lamar Alexander Andrew (Lamar) Lamar AlexanderGraham: GOP will confirm Trump's Supreme Court nominee before the election The Hill's Morning Report - Sponsored by Facebook - Washington on edge amid SCOTUS vacancy This week: Supreme Court fight over Ginsburg's seat upends Congress's agenda MORE (R-Tenn.) and Sen. Patty Murray Patricia (Patty) Lynn MurrayTrump health officials grilled over reports of politics in COVID-19 response CDC director pushes back on Caputo claim of 'resistance unit' at agency The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep MORE (Wash.), the ranking Democrat on the panel, are also working on legislation to stabilize the individual insurance markets.

Cornyn said Senate Republicans will decide at a private lunch meeting whether to hold a vote on the Graham-Cassidy bill, even though it’s clear the measure lacks the votes to pass.

“I don’t know how it all ends,” Cornyn said. “I know the work is going to continue but I think we need to turn to tax reform while that work [on health care] continues.”

Other Republicans on Tuesday said they’ll leave it up to Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellGraham: GOP will confirm Trump's Supreme Court nominee before the election Trump puts Supreme Court fight at center of Ohio rally The Memo: Dems face balancing act on SCOTUS fight MORE (R-Ky.) whether to hold a vote on Graham-Cassidy this week.

“That’s a call for leadership, I do not believe the votes are there,” said Sen. John Kennedy John Neely KennedyMORE (R-La.). “I think it’s time for us to move to tax reform. We clearly have to deal with the Affordable Care Act but I think we’ll have time to do that after we’ve done tax reform.”

Peter Sullivan contributed to this story.