Story highlights Because senators want to pass this bill with only a simple majority, it faces special restrictions

The House bill will have to go through what's known as the "Byrd Bath" in the Senate

Washington (CNN) The Obamacare repeal bill that passed the House Thursday moves next to the Senate where it faces daunting challenges because of the same ideological splits between conservative and moderate Republicans that nearly killed it in the House.

GOP leaders have set up a working group of senators across the ideological spectrum to try search for compromises that could unite enough Republicans to get the 51 votes needed for it to clear the chamber.

"There is 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, said Sen. Bob Corker, R-Tennessee, in an interview on MSNBC. "And I think you're going to see very responsible, deliberate action on it. People are going to want to improve it. I don't see anyway he comes back in the form it comes. It's not because I have any specific criticism of it."

One of the biggest challenges the House bill faces is that in order for it to be eligible for simple majority vote -- instead of a 60-vote threshold usually required for major bills -- it must meet special requirements under budget reconciliation rules. One of the key demands is that it lower the deficit. It is not known if the latest iteration of the House bill will do that, especially after money was added to it to resolve differences between the hard right House Freedom Caucus and the moderate Tuesday Group.

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