Some of those lawmakers have objected to sending tens of billions of dollars in aid overseas, without first passing funds for US-Mexico border security.
These conservatives have also dismissed as smears any suggestion that they could be Kremlin dupes.
President Joe Biden said in a statement on Wednesday he would sign the package into law immediately once passed by Congress “to send a message to the world: We stand with our friends”.
Ukraine is critically dependent on weapon supplies from the US and the West to keep fighting Russia, which has superior numbers and an abundance of artillery ammunition.
Months of congressional impasse have already had profound effects on the battlefield.
Ukraine has found itself outmanned and outgunned and forced into retreat because of ammunition rationing and falling morale.
In February, it retreated from Avdiivka, a town near occupied Donetsk that it had held since the conflict began in 2014.
Oleksandr Tarnavskyi, a general overseeing the withdrawal, cited a 10-to-one artillery ammunition advantage for his enemies and said pulling back after months of fighting was “the only correct solution”.
President Zelensky blamed an “artificial deficit of weapons” as he made urgent appeals for more military aid to avoid a “catastrophic” situation.
President Biden has cited “dwindling supplies as a result of congressional inaction” as a reason for the retreat.
Avdiivka’s loss was the heaviest for Ukraine since its troops pulled out of Bakhmut in May 2023.
Both came after months of attritional warfare in which Russian forces levelled buildings with massed artillery and poured waves of troops into the frontline.
General Sir Richard Barrons, a former commander of the UK’s Joint Forces Command, recently stated he feared that Ukraine could face defeat this year unless it was given the weapons and ammunition it needed to secure its lines.
“We are seeing Russia batter away at the front line, employing a five-to-one advantage in artillery, ammunition, and a surplus of people,” he said.
“Ukraine may come to feel it can’t win. And when it gets to that point, why will people want to fight and die?”
Both sides have suffered heavy losses in the battles but mounting casualties have left Ukraine, unlike Russia, with a shortage of manpower.
The government earlier this month lowered the age of conscription from 27 to 25 in an effort to raise hundreds of thousands of new recruits.
President Zelensky has said 31,000 Ukrainian soldiers have been killed since 2022. US officials, however, believe at least 70,000 have died and many more are injured.
A BBC investigation calculates that at least 50,000 Russian troops have been killed. Tens of thousands are believed to have been injured.
Russia has transformed its industrial base into a wartime economy – spending 40% of its national budget on armaments while striking deals with Iran and North Korea for ammunition, missiles and drones.