Story highlights "If they pass it, we will pass it," Cornyn told reporters

Senate leaders are working with a narrow margin to pass the bill, and can only afford to lose two members

(CNN) Republican Senate leaders will bring the House health care bill directly to the floor next week for a closely watched vote that will determine once and for all if Republicans can deliver on their seven-year promise to repeal Obamacare.

The Senate's second-ranking Republican leader John Cornyn of Texas, predicted Tuesday if the House passes its contentious health care overhaul bill when it votes Thursday, the Senate will take it up next week and pass it.

"If they pass it, we will pass it," Cornyn told reporters.

But getting the bill across the finish line may not be that simple.

The rapidly approaching vote -- even though it was previously announced -- drew words of caution from two key GOP senators who previously raised serious reservations about the bill and have not yet committed to vote for it.

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