Pelosi's Oval Office confrontation with President Trump Tuesday was also seen as a boost to her speaker candidacy. "Or we're going to get tremendous amounts of legislation passed working together", he said. "I will be the one to shut it down".
Pelosi said Trump does not have the votes in the House to secure the billions he wants to fulfill his promise to build a wall.
Pelosi later said: "This has spiraled downwards".
Democrats won back a majority in the House in November 6 elections.
"When the president brags he has won North Dakota and IN, he's IN real trouble", retorted Schumer with a smile.
Trump hinted on Tuesday that he has plans for the military to do more than just put up walling along property under the control of the Pentagon - he wants to use the money he insisted the troops needed for weapons of war to have service members building a far-reaching border wall.
Said Trump with a smile: "And then we have the easy one, the wall".
"For some time, there have been a number of conversations to advance a proposal to institute term limits for senior leadership positions in our caucus", Pelosi said in a statement announcing her support for the plan. "They know how important it is!"
"We gave the president two options that would keep the government open", Pelosi and Schumer said in a statement after the meeting.
"I am comfortable with the proposal and it is my intention to abide by it whether it passes or not", she said in a statement.
A group of Democratic senators had informed the Trump administration just yesterday that the military can not redirect funds to border wall projects.
House Democratic leader Nancy Pelosi and Senate Democratic leader Chuck Schumer are to discuss the wall and other issues with Trump on Tuesday. He later called the meeting a "good discussion". Asked to describe the atmosphere in the private meeting that followed the public quarrel, Pence said, "candid". The Kentucky Republican said "magic" sometimes happens in Congress ahead of Christmas, when lawmakers are eager to leave Washington. As such, I intend to fight alongside my colleagues to make sure the entire leadership team and future leadership teams are bound by this deal.
Rather than reach toward compromise, Trump tried to force Democrats to accept the border wall on his terms.
Pelosi is also commenting on the meeting's acrimony, noting "this has spiraled downwards". The homeland bill includes about $1.3 billion for fencing and other security measures at the border. According to AP VoteCast, more voters this year opposed the border wall than supported it. But Pelosi won a support pledge from the one Democrat who had publicly considered taking on the challenge: Ohio Rep. Marcia Fudge.
"It's not bad, Nancy - it's called transparency", Trump said.
At an appearance in Kansas City, Mo., Trump accused Democrats of playing a political game and said he ultimately would win.
Democratic Leader Nancy Pelosi announced Wednesday evening that she struck a deal with a group of seven rebel Democrats to limit the terms of senior Democratic leaders, paving the way for her election as House Speaker in January.
A woman carries her son near the border between the United States and Mexico, in Tijuana.
Democrats have signaled that they are willing to give Trump a third of the money he has laid out as a necessary for his wall but have stipulated that it can only be used for fencing.
He said party leaders are "people who've earned it" and added, "I don't see what problem we're trying to fix".
Trump is responding by saying he's "proud to shut down the government" and says he will "take the mantle".
The term limits would not extend to committee chairmen, a proposal that has been deeply controversial among House Democrats.