"We've proposed … that we come forth with a clean disaster package, a lot of things off including border security stuff, just disaster, basically. And the president said OK," Shelby told reporters after a closed-door GOP lunch.

Evan Hollander, Lowey's spokesman on the Appropriations Committee, said Lowey is supporting the agreement and wants to pass it through the House "as soon as possible."

"Chairwoman Lowey is pleased that President Trump and Republicans have agreed to bipartisan, comprehensive disaster relief legislation that will meet urgent needs across the country. If the Senate passes the legislation today, House Democrats support clearing it through the House as soon as possible," he said.

If the Senate was able to pass a disaster-only bill, the House — which is poised to leave town Thursday — could pass the legislation by a voice vote.