Most Democrats opposed the measure, but their opposition had nothing to do with the debt limit. Instead, they opposed the bill because it contains an unconstitutional provision that would delay salaries for members of the Senate and House if their chamber does not produce a budget by April 15. As stupid as the provision is, however, it won't have any practical impact on the budget process—budget resolutions are already required under current law. Nonetheless, the legislation could not have passed without Democratic support as 32 Republicans voted against it.
But while Republicans intended to score political points with their base with their "No Budget, No Pay" gimmick, they may have inadvertently exposed themselves by inserting the budget process into the debt ceiling vote. That's because their move allowed Democrats to offer an amendment to the legislation insisting that the House Budget protect senior citizens, veterans, and the active duty military from benefit cuts—and as you might have guessed, Republicans overwhelmingly rejected the amendment. In the end, just one Republican sided with
160150 Democrats who voted to oppose the cuts.
As for the debt limit, the measure basically eliminates the debt limit until May 19. Senate Majority Leader Harry Reid said that the senate would pass the measure as is. In theory, it would be possible for the GOP to stage another hostage crisis when the debt limit suspension expires, but after today's vote, any such move by Republicans would be an epic political meltdown. Just look at the title of the legislation they passed today: "A bill to ensure the complete and timely payment of the obligations of the United States Government until May 19, 2013." For Republicans to reverse course after May 19 would be to explicitly endorse default, and they are not going to do that. In practical terms, the debt limit hostage crisis is over, permanently. And the Boehner Rule—that every dollar of increase in the debt limit must be matched by a dollar in spending cuts—is dead, forever.
After passing the debt limit suspension, the House planned to vote to adjourn. Because in their world, working until Wednesday afternoon is like working until midnight on Saturday.
10:35 AM PT: To clarify, the bill suspends and raises the debt limit. It just doesn't specify precisely how much the limit will be raised. Instead, it authorizes the president to continue borrowing as needed in order to meet all obligations of the United States through May 19, 2013, at which point the debt limit will increase by the amount necessary to cover the borrowing that took place during the suspension.