Republicans had proposed amendments to prohibit implementation of the 2010 healthcare law, block funding to compensate federal workers for labor activities, and prevent the government from making new hires.
Earlier in the day, the White House said the sequester would force the White House to cancel these tours. But Republicans argued that Obama was making selective cuts in order to make the sequester as painful as possible, and could easily be cutting other parts of the federal government.
Democrats proposed two amendments to repeal or replace the sequester.
The House is scheduled to start work on the continuing resolution, H.R. 933, on Wednesday.