"I would say to my friends in the House of Representatives with whom I serve, do not walk the plank and vote for a bill that cannot pass the Senate and then have to face the consequences of that vote," Cotton said on ABC's "This Week."
He said that the bill "probably can be fixed" but said it will "take a lot of carpentry on that framework," referring to White House budget director Mick Mulvaney's comments earlier Sunday.
Mulvaney called the bill "a really nice framework" but said that the White House is "open to talking about" modifications.
"As it's written today, this bill in the House of Representatives cannot pass the Senate, and I believe it would have adverse consequences for millions of Americans and it wouldn't deliver on our promises," Cotton said.
He called for the House to "take a pause" and put more work into the bill before sending it on.
"I'm afraid that if they vote for this bill, they're going to put the House majority at risk next year," Cotton said. "I don't want to see the House majority put at risk on a bill that is not going to pass the Senate."