President Trump, not ready to back down on his campaign promise to repeal Obamacare, called up Senate Minority Leader Chuck Schumer Thursday to see if he could make any progress on the health care front.

Mr. Trump said he asked Schumer if Democrats "want to do a great health care bill," because Obamacare is "badly broken." Months of Republican attempts to repeal and replace the Affordable Care Act ultimately fell flat, and the GOP is looking elsewhere — like tax reform — for success.

I called Chuck Schumer yesterday to see if the Dems want to do a great HealthCare Bill. ObamaCare is badly broken, big premiums. Who knows! — Donald J. Trump (@realDonaldTrump) October 7, 2017

But Schumer isn't open to repealing Obamacare, something he said he made clear to the president. Mr. Trump last month shocked Republicans when he reached a deal with Schumer and House Minority Leader Nancy Pelosi, D-California, to extend the debt limit, suggesting he may be open to future deals with Democrats.

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"The president wanted to make another run at repeal and replace and I told the president that's off the table," Schumer said. "If he wants to work together to improve the existing health care system, we Democrats are open to his suggestions. A good place to start might be the Alexander-Murray negotiations that would stabilize the system and lower costs."

Through those negotiations, Senate Health, Education and Pensions Committee chairman Lamar Alexander, R-Tennessee, and the committee's ranking member Patty Murray, D-Washington, are looking to stabilize the health care market under Obamacare for the short term.

On the health care front, the Trump administration rankled Democrats Thursday when his administration announced employers and insurers with religious or moral convictions do not have to comply with Obamacare's mandate to cover birth control.

Mr. Trump has made it clear that he wants to return to undoing former President Barack Obama's signature health care law, despite Republicans' internal disagreement on how to repeal and replace it. But other legislative battles ahead may not be any easier for the Trump administration and Congress.

Retiring Sen. Bob Corker, R-Tennessee, said tax reform will make health care look like a "piece of cake," especially if the Republican Party wants to truly reform the complicated tax code, not just make a few tax cuts.

"Tax reform is going to make health care look like a piece of cake," Corker told reporters last month. "If we do it the right way, it hasn't been done in 31 years."