President Trump has been urging his Republican party to push the measure through both chambers of Congress so he can sign it into law.
He told House Republicans before they passed a version of the bill in February: “I’m not going to sign anything until this is approved.”
“It’ll guarantee the midterms,” he said, referring to November’s congressional elections. “If you don’t get it, big trouble, my opinion.”
Traditionally, the president’s party performs poorly in the congressional elections that fall halfway through their terms.
Explaining his support for the bill, Trump has also repeated his claim that the 2020 election was stolen by massive voter fraud.
While cases of small-scale voter fraud do occasionally emerge in US elections, no proof has emerged of such corruption on a scale that would alter the result of a White House vote.
Members of the president’s party, by and large, support the legislation in its original form.
Complicating the matter, Trump has attached additional provisions.
These include a proposed ban on postal ballots, with certain exceptions, such as for voters with disabilities or US military members.
But Republicans do not unanimously back a clampdown on mail-in balloting, which is popular in many US states.
Trump has also added other amendments unrelated to elections, in order to draw Republican support.
These include a ban on transgender surgery for children and on transgender athletes in women’s sports.