Republican Scott Garrett joined Democrats Frank Pallone, Rush Holt and Donald Payne in voting no.
The bipartisan measure easily passed the House Monday and is virtually assured to clear the Senate shortly after noon Tuesday by a wide tally.
The White House promises President Barack Obama will sign the measure into law.
Passage would avert a potentially disastrous first-ever default on U.S. obligations.
The legislation pairs an increase in the government's borrowing cap with promises of more than $2 trillion of budget cuts over the upcoming decade.