The comments of Jeffries came just after a closed door meeting of House Democrats, in which Speaker Nancy Pelosi urged rank-in-file Democrats to stick together on the shutdown, as Democrats continue to argue that no negotiations should take place on funding border security until the government has been funded.
While Democrats want the government to open first, Republicans, and the President, say the opposite should take place - that negotiations on border security should go first, before the partial government shutdown is ended.
GOP leaders scoffed at the idea that the State of the Union should be postponed simply because of the funding dispute, which began before Christmas.
"It doesn't matter what crisis America had in the past, we were able to still have a State of the Union," said Rep. Kevin McCarthy (R-CA), the House Republican leader.
House GOP leaders argued that Democrats were at fault for the partial shutdown - which has now stretched for 33 days - as they demanded that House Speaker Nancy Pelosi offer a plan for extra border security measures.
Not one time has Nancy Pelosi come forward with an alternative," said Rep. Steve Scalise (R-LA), the second-ranking Republican in the House.
While the House on Wednesday was ready to approve more funding bills from Democrats to fully fund the government, most eyes were still on the Senate, where leaders set two votes for Thursday - one on a GOP plan that mirrored the President's immigration proposal set forth last weekend, and a second plan from Democrats which would fund the government until February 8.
The White House has already threatened to veto that Democratic plan; officials on Wednesday morning issued a letter in which they said President Trump would sign the GOP proposal.
But Republicans would need the votes of seven Democrats to get 60 votes to proceed to that bill; for now, that seems unlikely.