Story highlights Senators aren't sure how much of the House GOP health care bill will be in their version

The chamber also needs to pass the bill under special restrictions due to reconciliation

Washington (CNN) The fight over repealing and replacing Obamacare now turns to the Senate, where a divided GOP conference will take up the House-passed bill and work over the next several weeks to find consensus to change it so it can both meet the chamber's unique rules and win the support of at least 51 Republicans.

Top GOP leaders say they plan an un-rushed and deliberative process to foster compromise between conservatives, who are anxious to repeal President Barack Obama's Affordable Care Act, and moderates who dislike it too but who are worried about the policy and political ramifications of not replacing it right.

In fact, Republican leaders don't plan to begin floor action until the Congressional Budget Office finishes formally scoring the House bill to determine its cost and impact on the uninsured. That could take at least two weeks, senators say.

"Now that the House has acted, it's timely for the Senate to act and we have every intention of doing that," said Sen. John Cornyn of Texas, the second-ranking Republican leader. "It's up to us to pass a bill that 51 senators can agree on."

What's not clear is how much of the House bill -- including its last-minute amendments dealing with coverage for people pre-existing conditions and extra funding for risk pools set up to assist them -- will make it into the final Senate bill. GOP senators aren't necessarily dissatisfied with those policies but warn they might not fit into the special demands of reconciliation, the special budget rules the Senate is employing to pass the bill because it allows them to do it with just 51 votes, not the 60 usually required for significant bills.

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