BATON ROUGE — U.S. Sen. John Kennedy said Tuesday that if he thinks the Senate GOP health care bill being negotiated behind the scenes is even a modest improvement over the federal health law he campaigned to repeal, he’ll support it.

Senate Republican leaders announced a reworked health care bill will be introduced Thursday, with a vote expected next week.

In office since January, Kennedy is seen as a likely supporter of any proposal to scale back the provisions of the federal health law. But he didn’t stake out a position on the first draft of the Senate bill and said he’s not yet sure if he’ll support the next draft because he hasn’t seen it.

He is ready, however, for the Senate to take a vote next week. And he said if he considers the proposal up for debate to be better than a current law he derided repeatedly when he ran for office: “Even if it’s not perfect, I’m going to vote for it.”

Kennedy gave the Senate 50/50 odds of passing health care legislation next week. He said if Republicans can’t pass a bill, he’ll be disappointed — but within limits.

“If we can’t reach an agreement on a bill, it’s not going to be the end of Western civilization,” the senator said in a conference call with reporters. “We can return to it, and we will.”

Gov. John Bel Edwards, a Democrat, has urged Kennedy and Louisiana’s senior senator, Republican Bill Cassidy, to oppose the draft of the Senate health bill that was released, saying it would devastate Louisiana’s health care system.

Extra money given to states that expanded their Medicaid programs to cover the working poor would be phased out, which Edwards said would force Louisiana to end the health coverage it provides to more than 430,000 people.

In addition, the governor objects to the proposal’s heavily scaled-back federal spending on the Medicaid program that existed before the Affordable Care Act. That program covers 1.2 million low-income people in Louisiana: pregnant women, children, elderly residents and people with disabilities.

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. Edwards and Louisiana advocacy groups have focused on Cassidy in efforts to jettison the Senate proposal.

Kennedy said the updated version of the Senate bill will include more money for states. He’s trying to negotiate several adjustments, though he wouldn’t say specifically what changes we wants made and suggested they wouldn’t cover all of Edwards’ points.

“I reviewed his letter very carefully. I understand his concerns. The legitimate ones we’re going to try to fix,” Kennedy said.