Republican senators are increasingly talking about the prospect of needing to amend the House’s health care law replacement bill.

Senate Republican Conference Chairman John Thune said it was entirely possible the Senate would amend the GOP health care bill through the budget reconciliation process on the floor.

“I think there’s got to be an opportunity for the Senate to be heard on this,” the South Dakota lawmaker said.

“There are lots of ways you can fix and amend the bill,” Thune said. “Then it would have to go back to the House, obviously, but I wouldn’t rule that out. I just think you’ve got to have an opportunity for members of the Senate to have their input into it.”

Thune made his comments to reporters following a meeting at the Capitol with Vice President Mike Pence on Thursday.

Republican Sens. Pat Roberts of Kansas and Rob Portman of Ohio also met with Pence, according to the vice president’s tweets.

If the plan passes out of the House, Senate Finance Chairman Orrin G. Hatch said the package would bypass his panel, with the major debate taking place as part of the reconciliation vote-a-rama on the floor.

“The Senate will just take it up,” the Utah Republican said Wednesday.

Republican Sen. Tom Cotton of Arkansas said early Thursday morning he thought the House GOP should not be moving so quickly.

“What matters in long run is better, more affordable health care for Americans, NOT House leaders’ arbitrary legislative calendar,” Cotton said on Twitter.

The differences between the needs of House and Senate Republicans may become more problematic if the House bill moves in the direction of imposing further restrictions on the expansion of Medicaid provided under the 2010 health care overhaul.

Portman said in a statement that he discussed the Medicaid issue with Pence during their Thursday morning meeting. A group of 50 Republican senators would need to come together to back any final bill, with Pence as a potential tie-breaker.

“I appreciated the opportunity to address my concerns about our Medicaid expansion population in Ohio. As I have said before, I support making structural improvements to the Medicaid program, but we must provide stability and certainty for individuals and families in Medicaid expansion programs and real flexibility for states,” Portman said. “I will continue to work with the administration and my colleagues to address these concerns.”

Sen. Shelley Moore Capito, a Republican from the Medicaid expansion state of West Virginia, said she had just heard about the prospects of the White House backing any House move to impose additional curbs on the benefits.

“I’ve just heard that’s bubbling up. That causes me great concern, and I will be talking with my fellow senators who are more deeply affected by this, of course, in the expansion states,” Capito told CQ Roll Call. “I have grave concerns about that.”

She said she was already planning to talk with Health and Human Services Secretary Tom Price over the coming weekend.

Meanwhile, elsewhere on Thursday morning, Senate Majority Leader Mitch McConnell was somewhat dismissive of conservative outside groups coming out against the health care bill.

“Everybody can weigh in. That’s the way the legislative process works,” the Kentucky Republican said at a Politico Playbook interview.

McConnell noted that many Republicans have not served under a GOP president before.

“We need to get into a governing mode and start achieving something, rather than just kind of sparring,” he said.

Alan K. Ota and Bridget Bowman contributed to this report.