The plan, introduced Thursday, calls for spending $500 million to reimburse local agencies that scrap their electronic voting machines in favor of paper.
''Voters should never have to leave their polling places wondering if their legitimate vote will be counted,'' said Rep. Rush Holt, D-N.J.
New Jersey is one of 20 states that could benefit under the bill, The Miami Herald reported Friday.
Rep. Robert Wexler, D-Fla., has long pushed for paper ballots.
He pointed to the contested congressional race in Sarasota, Fla., to make his point that a paper trail is necessary to restore ''reliability, accessibility and credibility'' to elections.
Holt has also introduced a bill that would require states to move to paper ballots, but it has yet to be heard on the House floor, the newspaper reported.
He said he has no promise from the House leadership that it will come up with the proposed $500 million to reimburse the states, but said he is "confident it will be available."
Notable deaths of 2014 [PHOTOS]