WATCH: Dem senators make the case for the very bill they're trying to kill

"The evidence is that almost no illegal aliens vote," Schumer said in remarks on the Senate floor.

Warnock similarly acknowledged the issue while listing statistics about voting records in his home state.

Democrats have fiercely opposed the Republican-led bill, citing concerns that its voter integrity measures are overly heavy-handed and could inadvertently burden communities that may struggle to provide documented proof of citizenship.

"This is a solution in search of a problem that does not exist," Warnock said.

Under the bill, voters could use a REAL ID, a birth certificate or a passport to satisfy the requirements, according to the bill's text.

"Democrats argue that federal law prohibits noncitizen voting and insist that it is not just rare but exceedingly rare - so rare that we shouldn't even consider it cognizable in this chamber," Lee said Tuesday.

Lee said the lack of documented cases does not rule out future risk.

"It remains unknown - and in many instances, unknowable. How many illegal votes are being counted in federal elections? How many illegal votes cast by noncitizens might be cast in any future federal election?" Lee said.

The standoff, which began Tuesday, appears unlikely to advance the bill.

Fox News Digital reached out to the offices of Schumer and Warnock.