Senate Minority Leader Charles Schumer (L) ,D-N.Y., looks on as House Minority Leader Nancy Pelosi, D-Calif., speaks to reporters during a news conference at the U.S. Capitol in Washington.

President Donald Trump on early Friday morning suggested congressional Democrats "call me to fix" Obamacare, hours after his administration announced a potentially crippling move against that health-care law.

Trump's tweet, and a published report, suggest the president may be open, via a bipartisan deal, to restoring the billions of dollars in crucial federal payments to insurers that he had suspended.

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Soon afterward, Trump posted another health-care tweet.

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"You are going to have great health care in our country," Trump said Friday morning during his speech at the Value Voters Summit, after those two tweets.

"We're taking a little different route than we had hoped because Congress — they forgot what their pledges were," Trump said, referring to the failure of the Republican-led Congress to pass an Obamacare repeal bill.

"In the end, it will be just as effective, and maybe even a little bit better," Trump said, referring to an executive order he had signed on health care on Thursday morning.

Trump's executive order directed multiple federal agencies to look into making changes to health-care regulations that relate to the issuance of insurance plans by small businesses, and short-term health coverage plans.

Obamacare advocates were outraged by that move — but it was not clear how much damage the order would actually end up doing to Affordable Care Act insurance programs.

On Thursday night, the Trump administration announced it would "immediately" cease making billions of dollars in subsidy reimbursement payments to insurers.

There is widespread agreement that the move will lead to higher premiums, a potential exodus of insurers from the Obamacare markets and add almost $200 billion to the federal deficit.

Obamacare defenders, already fuming about the earlier executive order, unleashed anger online after Trump's decision to kill the payments.

However, shortly after the announcement, The Wall Street Journal reported that Trump "has privately told at least one lawmaker that the payments may continue if a bipartisan deal is reached on heath care."

Sen. Lamar Alexander, R-Tenn., and Sen. Patty Murray, D-Wash., have been trying to reach such a deal, which would ensure continuation of the so-called cost-sharing reduction payments.

The payments, which were projected to be worth $10 billion to insurers next year, reimburse sellers of Obamacare health plans for discounts that are offered to low-income customers for their out-of-pocket medical expenses, such as copayments, deductibles and coinsurance.

Those discounts must be granted by insurers by law to qualified customers.

The Obama administration had, for years, reimbursed insurers for the cost of the discounts despite the fact that the Republican-led Congress refused to specifically authorize that spending. When Trump took office, the payments also continued, for months, despite House Republicans having won a federal lawsuit that challenged the legality of the payments, and despite the president's stated virulent opposition to Obamacare.

Both the Trump administration and House Republican leaders had effectively agreed to continue allowing the government to make the payments as an appeal of the lawsuit, first made by the Obama administration, remained pending.

That changed Thursday night, after U.S. Attorney General Jeff Sessions provided an opinion that the payments were illegal, leading the administration to say the payments would end.