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Republican Sens. Ted Cruz of Texas, Mike Lee of Utah and Tim Scott of SC all publicly said Thursday they hadn't decided whether to back McConnell's reworked bill.

Work on the Senate's health-care bill remained uncertain Tuesday, though McConnell told reporters he will release a revised bill by Thursday morning and hopes to receive a Congressional Budget Office analysis of that measure by the beginning of next week so the chamber can vote quickly.

"It would be like the Wild West of health care", he said.

With his reputation as a master strategist on the line, majority leader Mitch McConnell laid out a timetable for Senate consideration of legislation that would fulfill the Republican president's campaign promise to dismantle the Obamacare law. Republicans can only lose two votes and still pass the bill.

Looks like the Senate health care bill may not cut Obamacare's taxes on the rich. The proposed health care bill does nothing to address the cost of healthcare and the cost of pharmaceuticals.

McConnell was expected to appeal to those senators by adding $70 billion to a stabilization fund to help lower-income people pay for medical costs, a $45 billion fund to combat opioid addiction and the extension of the current 3.8 percent tax on the wealthy.

McConnell said that he plans to release the revised bill later this week and hold a key procedural vote early next week.

But Senate Majority Leader Mitch McConnell still faces the challenge of securing enough votes from conservatives and moderates with differing concerns to push the bill through. Voters are also divided on President Donald Trump's role in the ACA repeal and replace process, with 27 percent saying the president has been too involved in efforts to pass the bill. At least eight GOP senators still oppose the plan as written now.

Cassidy, a doctor who worked for years in Louisiana's charity hospital system, is seen as more open to bucking GOP leadership on the health law rewrite because of his criticism of similar legislation passed by the U.S. House.

Trump's distance from health care has come after senators and their top aides have made it clear to the White House that the less Trump is involved in detailed negotiations, the better they believe the prospects are.

Paul also called the insurance company bailout included in the Senate Republican bill a "terrible idea".