Most Democrats are opposed to the supplemental funding request, and there is discontent in Republican ranks too.
Some of the fiscal hawks in the Republican Party want spending cuts elsewhere to offset the budget.
Either way, the House of Representatives leaves town on Thursday and the two chambers of Congress will not be jointly back in session until September.
Even if Republicans can muster the votes, it’s going to be a couple of months before the Pentagon can get the funds.
The defence department on Tuesday announced the death of Sgt Michael Emmanuel Swinton, a 30-year-old active-duty soldier who was supporting overseas operations in Iraq.
A day earlier, the military identified two US service members killed in action in Jordan as Pfc Isabella Gonzales, 19, and 1st Lt Tyler Feehan, 25.
During the hearing, Trump – who was not present – posted a list of US wars on social media, including how long they took to end and how many US soldiers died. He wrote that 18 had died in the US war with Iran, which began on 28 February.
