The incident occurred Tuesday evening as the House prepared for its customary round of 6:30 p.m. votes, The Hill reported.
"We all exchanged stories. We had a nice talk," Rep. Marsha Blackburn, R-Tenn., told the newspaper.
Aides had to pry the doors open once the car made it halfway up to the second floor. Lawmakers then climbed out.
"It was a very dignified exit," Rep. Mike Conaway, R-Texas, said.