"In the meeting, the President and Congressional leadership agreed to pass aid for Harvey, an extension of the debt limit, and a continuing resolution both to December 15, all together", Schumer and Pelosi said in a statement after the meeting.
"I'm glad that some Republicans in Congress have voiced their opposition to the President's decision, because we're going to need them to right the ship", Schumer said.
Trump described the meeting to reporters on Air Force One: "We had a very good meeting with Nancy Pelosi and Chuck Schumer". He wouldn't say if he was surprised by the deal, but said Trump's "rationale" was the "feeling that we need to come together".
Earlier in the day, Republican House Speaker Paul Ryan had called the Democratic proposal for a three-month increase "a ridiculous idea" that would "play politics with the debt ceiling".
Trump's deal ensures the government can borrow money and pay its bills into December in exchange for $8 billion in Harvey aid..
A separate aide, who was also briefed on the meeting, said Republican leaders pushed for an 18-month debt limit hike before floating six months.
Those include Harvey disaster relief, raising the debt ceiling by early October to prevent an unprecedented default on USA government debt, and passing legislation for federal spending in the fiscal year that begins on Oct. 1 to avoid a government shutdown.
It's a major development given the pressing list of tasks Congress had to take on over the next month and the fact that Trump sided with Democrats' desires over those of Republicans. That's the objective of a debt limit.More news: American Horror Story: Cult Season Previews Tease New Episodes
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Pelosi and Schumer said in their statement that "we also made it clear that we strongly believe the DREAM Act must come to the floor and pass as soon as possible and we will not rest until we get this done".
The deal includes Democratic support in the Senate for the first instalment of disaster relief aid for Hurricane Harvey victims in Houston, where flooding has devastated the Texan city.
Republican leaders also wanted to raise the ceiling, but with a much longer timeline-through next year's midterm elections-so they could avoid another painful vote on the issue that has divided their members between those who want a "clean" hike in the government's borrowing authority and those who want to use the debt ceiling to pass more spending cuts.
Nebraska Republican Senator Ben Sasse was one of them, saying in a tweet that "The Pelosi-Schumer-Trump deal is bad". The House approved the measure in a 419-3 vote.
The House-passed bill would provide $7.4 billion for the Federal Emergency Management Agency and $450,000 for the Small Business Administration.
The meeting was created to discuss legislation to provide relief for Hurricane Harvey, raise or suspend the debt ceiling, and fund the government past the end of September. That may help Ryan gain votes of conservative lawmakers when the legislation comes back from the Senate. Both groups oppose linking the debt ceiling to disaster funds.
Meanwhile, congressional Republicans are left fuming. Republicans would have preferred a longer debt ceiling extension to avoid giving added leverage to Democrats negotiating in December.