She also says the president "is incredibly disappointed" with Republicans who voted against him.
While Congress is unlikely to muster the votes to override the veto, the rebuke from some members of his own party left Trump politically wounded, at least temporarily, as immigration and his planned wall along the USA southern border become a flashpoint again in the 2020 presidential campaign.
Alexander added that he shares the president's goal of border security, but warned allowing Trump to redirect money without authorization could set a unsafe precedent.
Trump expressed pride in the Republicans who did not vote to support the resolution and said later that he had sympathy for those who defied him, adding they did what they had to do.
Senate Democrats, who have consistently opposed many of Trump's hardline immigration policies, were joined by Republicans who expressed support for Trump's calls to build a wall - but cited concern about the expansion of presidential power.
"We're bursting at the seams, we can only hold so much", he said.
Republicans, Pelosi said, "will have to choose between their partisan hypocrisy and their sacred oath to support and defend the Constitution". In a statement, Republican senator Lamar Alexander of Tennessee said: "Never before has a president asked for funding, Congress has not provided it, and the president then has used the National Emergencies Act of 1976 to spend the money anyway".
The emergency declaration is being challenged in court as an unconstitutional usurpation of Congress' power of the purse. Democrats deny there is an emergency at the border, saying border crossings are at a four-decade low.
Trump insists he's on solid legal ground, however. "I think the value of these last few weeks is to remind the Senate of our constitutional place". "Ideally, they shouldn't even sue in this case, if you want to know the truth".
On Friday, Barr also said the president's emergency order was "clearly authorized under the law".