Democrats voted, 196-173, to table the measure shortly after Boehner offered it, preventing their members from having to cast a vote to protect the outspoken California liberal. Boehner and his Republican colleagues were hoping to re-ignite coverage of Stark's controversial remarks.
After the vote, Stark apologized to the House and the president for his inflammatory comments last week.
"I want to apologize to my colleagues, many of whom I have offended," Stark said on the House floor. "I hope that with this apology I will become as insignificant as I should be, and that we can return to the issues that do divide us but that we can resolve in a better fashion."
The California Democrat teared up as he closed to the applause of lawmakers in the chamber.
Stark made his comments last Thursday during an otherwise muted debate over the vote to sustain President Bush's veto of a bill to expand the popular state-run children's health care program that has become the dominant policy fight this fall.