The deal would attach both the short-term government funding and the debt limit increase to the House bill.
The resolution continues government operations and raises the debt ceiling until December 15, when Congress will have to vote on the issue again. The bill did not yet include the debt limit or government funding.
The federal government is running out of borrowing authority, which officials say must be increased to pay for existing obligations, including hurricane relief efforts.
The U.S. Senate on Thursday approved $15.25 billion in aid for areas affected by Hurricane Harvey and other natural disasters, along with measures that would fund the federal government and raise its borrowing limit through December 8.
Republicans were advocating for a suspension of the debt ceiling of either six or 18 months.
President Trump offered assurances to DACA recipients on Twitter Thursday at the request of House Minority Leader Nancy Pelosi, an aide told Fox News - in the latest example of the president's new outreach to Democrats. We've got another unprecedented hurricane about to hit Florida.
"That will strand the aid that we need to bring to the victims of these storms that have occurred or about to occur and they also want to threaten to default on our debt?" he asked. "To play politics with the debt ceiling like Schumer and Pelosi are apparently doing I don't think is a good idea". That would depend, however, on whether House Speaker Paul Ryan (R-Wis.) allowed it to go for a vote. Trump cut him off and abruptly sided with Schumer and Pelosi on their three-month request.
Mr. Trump, however, improvised and took the deal for three reasons, Garrett reports.
The president's decision gives Democrats a victory and leverage to push for other legislation they deem of top importance.
Trump said Thursday that the debt ceiling is a "sacred trust" and "as long as it's there, it will never be violated".
The appeal of Trump for lots and lots of voters - especially Republicans - was that he had, quite literally, written the book on deal-making.