"No chance the House will come back early," the source said on Friday.
"The Senate doesn’t dictate the will of the House."
House lawmakers departed Washington on Thursday to begin their holiday recess through January 3. The Senate, which was set to go on recess on Friday, will instead reconvene next week with hopes of reaching a deal on passing the supplemental package that includes more aid for Ukraine and Israel.
US Senate Majority Leader Chuck Schumer said the Senate could vote on the supplemental bill sometime next week if a deal is reached between Senate Republicans and Democrats and the White House.