Story highlights Sens. Lamar Alexander and Patty Murray have sought a health care deal

President Donald Trump's announcement last week added new urgency

(CNN) Tennessee Republican Sen. Lamar Alexander said Monday he's getting encouragement from both President Donald Trump and Senate Minority Leader Chuck Schumer to reach a health care deal soon that would restore cost-sharing reduction payments in exchange for state flexibility on some plans.

"The President has encouraged me to try to get an agreement with Sen. Murray," Alexander told reporters, a reference to Sen. Patty Murray of Washington, the top Democrat on the Senate's health committee. "Sen. Schumer has encouraged me to try to get an agreement with Sen. Murray. I find that very encouraging when both the President and Sen. Schumer encourage me to do something."

Alexander confirmed to reporters Monday that he spoke to Trump over the phone Saturday about restoring the CSR payments and that the President was supportive of him reaching a deal, something even some GOP colleagues have resisted.

For weeks, Alexander has been working with Murray on legislation that would appropriate CSR payments for two years in exchange for state flexibility, but after Trump announced Thursday that he would stop making the payments himself their negotiations have been met with even more urgency.

Without CSRs -- funding the federal government gives to insurers to reduce health care costs of low-income people -- health care experts have warned that insurers could leave the Obamacare marketplace or raise premiums in the future. Alexander and Murray have tried to negotiate a plan that would require Republicans to agree to fund CSRs if Democrats agreed to allow states to offer some insurance plans that did not comply with some Obamacare regulations.

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