Officials have also warned that a repeal measure would run the risk of being watered down by amendments.
As President," she asked, "would you veto a repeal measure?
White House aides indicated that President Bush would sign the repeal measure.
All four voted for the original repeal measure.
The original repeal measure passed by 28 votes.
The Senate approved the repeal measure last week in an 18-to-17 vote, but the House's reversal today was unquestionably the final step.
A previous version of the repeal measure won 55 favorable votes, also one more than needed to override.
But the repeal measure is unlikely to go any further.
Topeka voters defeated the repeal measure on March 1, 2005, by a 53-47% margin.
For that reason, the repeal measure has the support of many municipal officials.