President Donald Trump will meet with the two top Democrats in Congress sometime this week as the federal government heads toward a possible shutdown, a person familiar with the meeting told CNBC.

Trump's meeting with Senate Minority Leader Chuck Schumer and House Minority Leader Hakeem Jeffries, both New Yorkers, would come just days before a Sept. 30 deadline for Congress to pass a funding resolution that would keep the government open.

Prospects for such a deal, as of now, look dim as Democrats hold firm on demands that any resolution include an extension of the Affordable Care Act's enhanced tax credits.

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