On Sunday, the bill got a boost when the Senate voted 67-27 to move it past an important procedural hurdle. Also over the weekend, Majority Leader Chuck Schumer set a course for passage by Wednesday.
On Monday, the Senate is expected to cast a procedural vote that, if successful, would keep the bill moving forward.
Having kept senators working during rare back-to-back Saturday and Sunday sessions, Schumer wrapped up for the night saying, "Our friends abroad are watching closely how we vote in the upcoming days. Ukrainian fighters are watching and you can be sure (Russian President) Vladimir Putin is watching the Senate, too."
Since last August, Democratic President Joe Biden has been urging Congress to hurry new aid to Ukraine. Following Hamas' Oct. 7 attack on Israel he also requested funds for the U.S. ally along with humanitarian aid for Palestinians in Gaza.
Congress' haltingly slow response to Biden's call comes as Ukrainian officials have warned of weapons shortages at a time when Russia is pressing ahead with renewed attacks.
"There's no good reason to delay the security and humanitarian assistance ... any longer," Senate Foreign Committee member Brian Schatz, a Democrat, said during Sunday's debate of the bill.
"Ukraine is running dangerously low on munitions on the eve of the second anniversary of Putin's invasion," added Schatz. "Millions of innocent Palestinians in Gaza are suffering daily without access to basic necessities."
The bill now being debated in the Senate has drawn opposition from some Republicans, including in the House of Representatives, who want to shut off U.S. aid to Ukraine. At the same time they are insisting that the southern U.S. border with Mexico be hardened to stop an unusually high flow of undocumented immigrants.
But last week, at the urging of former President Donald Trump, most Senate Republicans voted to kill a bipartisan border security bill that had been crafted over four months. It was seen as the most significant border security and immigration reform effort in at least a decade.
Following last week's action, Schumer stripped the border security language from the legislation and has advanced a bill providing the aid to Ukraine, Israel and Gaza, as well as Taiwan.
Republican Senator Lindsey Graham, in a Senate speech, called for yet another overhaul of the bill to reflect some of Trump's desires.
Graham said portions of the U.S. aid should be converted into loans and only "lethal aid," not humanitarian aid be included in the package. And he called for U.S. border security provisions, although so far his party has not unveiled border-related amendments.
(Reporting by Richard Cowan; Additional reporting by Patricia Zengerle; Editing by Don Durfee and Christopher Cushing)
By Richard Cowan