Sen. Bill Cassidy (R-La.) said in an interview broadcast on Sunday that he wants the healthcare bill to be negotiated with both parties.
"I wish we weren't doing it one party. But that said, if you can lower premiums, that is common ground," Cassidy said on NBC's "Meet The Press."
"Turns out to lower premiums, there's ways you do that. You get more people into the risk pool so it's healthier and younger, number one."
Cassidy added that people who have lower income are going to "need some assistance."
"And so you need money for that assistance," he said. "And for those who are perhaps richer, you relax a few of the regulations, not too many, but hopefully make it so that they can better afford."
Cassidy was also asked during the interview whether he thinks something can be done on healthcare that still unites 50 Senate Republicans.
"I think something can be done," Cassidy said.
"If you go back to the president's intuitions and his campaign pledges, he wants to cover everybody, care for those with pre-existing conditions, eliminate mandates, lower premiums. That's actually a place that you can get common ground."
Senate Republicans last week decided to delay a vote on their healthcare bill after it became clear it lacked the votes for passage.
Amid GOP disunity over the health plan, President Trump on Friday floated repealing former President Obama's signature healthcare law before moving later on a plan replace it.
Cassidy faced backlash over the Senate ObamaCare repeal bill last week at a town hall, where he noted he remains undecided on how he will vote.