The legislation would fund homeland security operations until February 8 and several other agencies through September.
Trump has said he would veto any bill, however, that does not include funding for the wall and the Republican-run Senate has said it would not consider any legislation that does not pass muster with the president.
The fight over the wall is setting the stage for what could be a tumultuous final two years in office for Trump faced with a hostile Democratic-controlled House equipped with investigative powers.
Some newly seated Democrats have even called for impeachment proceedings against the Republican president but Pelosi has distanced herself from those appeals.
“We shouldn’t be impeaching for a political reason, and we shouldn’t avoid impeachment for a political reason,” she told NBC’s Today show. “So we’ll just have to see how it comes.”
Trump lashed out on Friday at the mention of impeachment.
“How do you impeach a president who has won perhaps the greatest election of all time, done nothing wrong,” he said on Twitter, throwing in a claim that he has had “the most successful first two years of any president.”