Trump warns he won't endorse lawmakers who oppose Save America Act

"The Save America Act is one of the most IMPORTANT & CONSEQUENTIAL pieces of legislation in the history of Congress, and America itself," Trump wrote.

"I WILL NEVER (EVER!) ENDORSE ANYONE WHO VOTES AGAINST 'SAVE AMERICA!!!'"

Trump said the bill also touches on issues including mail-in voting, transgender athletes and medical care for minors.

"No Men in Women's Sports, No Transgender MUTILIZATION of our Children. 90% to 99% ISSUES ALL! Only sick, demented, or deranged people in the House or Senate could vote against THE SAVE AMERICA ACT. If they do, each one of these points, separately, will be used against the user in his/her political campaign for office - A guaranteed loss."

The GOP-led House passed the bill in February, largely along party lines.

Trump and his allies argue the legislation would prevent noncitizens from voting and strengthen election security, while critics say it could disenfranchise eligible voters who lack documentation.

The bill now faces steep odds in the Senate, where it would need 60 votes to overcome a filibuster - a threshold Republicans do not currently have given their 53-47 majority.

"It's about the math," Thune said. "And I'm, for better or worse, the one who has to be a clear-eyed realist about what we can achieve here."

Republicans are expected to force a vote to put Democrats on record opposing the bill, but the measure faces steep odds of clearing the Senate's 60-vote threshold.

Sen. Lisa Murkowski, R-Alaska, has also come out against the bill, warning that new federal mandates could disrupt state election systems.

Fox News' Alex Miller and Elizabeth Elkind contributed to this report.