At a Democratic National Committee rally, Mr Biden suggested the two extra Democrats would allow the Democratic-controlled Senate to remove a legislative roadblock known as the filibuster that requires a 60-vote majority to overcome.
Democrats hold a bare majority in the Senate now, and two Democratic senators, Joe Manchin of West Virginia and Kyrsten Sinema, have opposed ending the filibuster.
Mr Biden’s remark suggests he would support a vote to end the filibuster, which can be decided by a simple majority. For any such move to be successful, Democrats need to retain control of the House and gain two seats in the Senate. Most forecasters suggest Republicans are likely to gain House control.
Mr Biden has made restoring protections lost in the Supreme Court’s June decision to reverse the landmark 1973 Roe v. Wade case a central theme of his stump speeches in the lead-up to the November 8th congressional elections.
“If you give me two more senators in the United States Senate, I promise you, I promise you, we’re going to codify Roe and once again make Roe the law of the land,” said Mr Biden.
Mr Biden exhorted women voters to help elect Democrats.
“I don’t believe the MAGA Republican have a clue about the power of American women. Let me tell you something, they’re about to find out.”
According to the Current Population Survey, 2020 voter turnout was 68.4 per cent for women and 65.0 per cent for men. About 9.7 million more women than men voted. Since the Supreme Court decision on Roe, there has been a surge in women registering to vote.