Sen. Bob Corker anticipated it could take about a month before the Senate is ready to move on health care, although he conceded Thursday morning that he largely focused on other issues after the previous failure of the House legislation. He also predicted changes in the Senate.

“There’s a working group over here of Republicans with, you know, with a range of ideology that are working to see where we go with the bill when it comes across. And I think you’re going to see very responsible, deliberate action on it,” the Tennessee Republican said on MSNBC. “People are going to want to improve it. I don’t see any way that it goes back in the form that it comes. And it’s not because I have any specific criticism. I just know that, over here, people want to make sure that it’s something that’s going to work for the American people.”

But the legislation could run into additional procedural hurdles. Democrats believe that several provisions in the bill would be ruled out of order because they do not have the kind of deficit effects required under the Senate’s Byrd Rule that’s crucial to using the budget reconciliation process to pass the bill with a simple majority.

Senate Minority Leader Charles E. Schumer singled out in particular a late-addition to the bill that would allow states to apply for a waiver out of several of the law’s coverage requirements, as well as another amendment that would provide states more money to help cover those individuals with pre-existing conditions.

“Its chances for survival in the Senate are small. We don’t even know if the new version would survive under the rules of reconciliation,” the New York Democrat said on the Senate floor on Wednesday.