In that scenario, Congress would pass 6 of the 7 remaining appropriations bills for 2019, and a continuing resolution (CR) for Homeland Security, the bill that deals with border security funding.

That position may put House Democrats slightly at odds with their Senate counterparts.

Schumer reiterated the option on the Senate floor Thursday, shortly ahead of Pelosi's remarks.

“This is something Democrats have always been for: Smart, effective, appropriate border security. This is so good that every Republican appropriator signed off on that bill a few months ago,” he said. He also reiterated that the funds could only be used for certain kinds of fencing, and not a concrete wall.

Trump has demanded $5 billion to fund the wall, an amount that House Republicans passed in their version of the Homeland Security bill earlier this year.

Even a CR, however, would renew the 2018 funding level of $1.6 billion designated for border security.