Sen. Lamar Alexander acknowledges that the final tax bill set to pass this week will increase health insurance costs for those who use the federal exchanges. But he says his bipartisan bill to stabilize the insurance marketplace will offset the cost increase.

The tax bill ends the individual mandate for everyone to buy insurance, which would likely mean many healthy people would drop their coverage, making marketplace customers a sicker bunch more costly to insure.

Still, the Republican chair of the Senate’s health committee is glad to see the mandate go.

“That’s good news for most Tennesseans because it means you don’t have to pay a penalty for insurance you don’t want to buy. But it will also slightly create upward pressure on premiums,” Alexander said Friday after speaking to the Brentwood Rotary Club. “But the Alexander-Murray legislation will push rates down a lot further than repeal of the individual mandate will push them up.”

Alexander’s bill written with Sen. Patty Murray, D-Washington, would restore subsidies to insurance companies that offer plans on the marketplace. They’re known as “cost-sharing reduction payments” and help offset the out-of-pocket costs for some marketplace participants, above and beyond the tax credits to cover monthly premiums.

Under the Alexander-Murray proposal, states also have the option to get waivers from some of the Affordable Care Act’s rules, like allowing insurance companies to offer less comprehensive plans. The bill also restores advertising budgets for the marketplace’s open enrollment period.

There is some doubt that the Obamcare fix would paper over the effects of eliminating the individual mandate. The left-leaning Center on Budget Policy Priorities says “nothing in the Alexander-Murray bill can undo the damage that would result from repealing the individual mandate.”

According to Alexander, Senate Majority Leader Mitch McConnell has “pledged” to put the Alexander-Murray compromise into the spending bill that should be voted on later this week. Alexander believes he also now has support from President Trump, even though the president has previously called it a “bailout” for insurance companies.

The House of Representatives would also have to agree to include the provisions in the spending bill, which already includes a number of controversial proposals that could be tacked on.

“We’re very hopeful that the House will agree to it since most House members have already voted for similar provisions in the repeal-and-replace legislation earlier this year,” Alexander said. “It will stabilize the insurance market.”

WPLN’s Meribah Knight contributed to this report.