The comments came as top Democrats continued to refuse to negotiate with Trump, who said he was open to reaching a compromise on the amount of money for the wall but that he wouldn't agree to a deal with no wall funding in it.
Congressional leaders from both parties held unproductive talks with Trump at the White House on Wednesday and are to return for another round on Friday, a sign the shutdown is likely to continue for the rest of the week.
For the White House, the final position is more ambiguous: Vice President Mike Pence put a proposal for $2.5 billion for a combination border security and immigration priority funding on the table last week, but was rebuffed by Schumer.
"We can go through this all back and forth - no", Pelosi added.
After those actions, House Democrats will move quickly to vote on spending bills to reopen the federal departments and agencies that have been closed since December 22, without providing funds for Trump's wall on the Mexican border.
For Democrats, that means they will not put anything on the table beyond the current $1.3 billion for border security.
Democrats have made an offer on the budget, but it doesn't include funding for a wall.
Senator Majority Leader Mitch McConnell later said that no progress was made Wednesday in the meetingwith Trump.
Democrats wasted no time flexing their new power in the U.S. House of Representatives on Thursday as they manoeuvred to pass legislation backed by new Speaker Nancy Pelosi that would end a 13-day partial government shutdown while ignoring President Donald Trump's demand for $5 billion for a border wall.More news: NASA Makes Space History With Distant Fly-By
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Once the secretary started, Senate Minority Leader Chuck Schumer (D-N.Y.) interrupted her, McCarthy said.
The partial government shutdown began on December 22 after Trump refused to sign a budget deal that didn't include billions of dollars for his long-promised and long-stalled southern border wall. Democrats oppose the wall and Trump's funding demand.
So the standoff rumbles on and so will the partial shutdown.
Trump later reiterated: "The $5.6 billion is a small number".
Sanders described that approach as a "non-starter because it does not fund our homeland security or keep American families safe from human trafficking, drugs and crime". In FY 2017, there were about 310,000.
But a NPR/PBS Newshour/Marist poll taken before the shutdown began had a different finding. Funding for the wall has been the sticking point in passing essential spending bills for several government departments.
With Democrats taking control, it's unclear if their leadership will pursue impeachment ahead of special counsel Robert Mueller's final report on his probe into Mr. Trump and potential conspiracy with Russians during the 2016 election.
She said it was an "open" legal discussion whether Trump could be indicted while still in office.
Pelosi, a liberal who represents San Francisco, will lead a House with 235 Democrats, 199 Republicans and one seat in North Carolina still being contested.