The president's budget will be offered as a substitute amendment Tuesday.
Senators voted 94-3 for an amendment from Sen. Bernie Sanders opposing Medicaid cuts.
Reading bills aloud on the House floor is typically a routine and monotonous process. But not so for Rep. Rob Woodall (R-Ga.).
The budget amendment to boost spending was rejected in a 45-52 vote.
Rep. Robert Dold (R-Ill.) said he "can't think of a worse message."
The Ohio Republican's budget amendment would create a deficit neutral fund.
"That money isn't close to being real," the Senate minority leader said.
Leaders of both parties claim they are the ones standing with the middle class.
House and Senate lawmakers are working on their budget resolutions.
The Obama administration has so far only provided non-lethal support to Ukraine.