... you thought wrong.
House Republicans and Democrats both have some interesting little tricks in their political bags.
The Republican trick is to propose a "moderate/reasonable" budget-balancing path, then count on all the Democrats to vote against it, so that only a few Republicans have to pretend to jump ship to kill it (after which, they blame the Democrats for its failure to pass).
The Democrat trick is to get most Democrats to just vote "present," in the hope that the Republicans will pass said "moderate/reasonable" budget-balancing path (which Democrats consider "extreme"), after which it will die in the Senate or under the president's veto stamp (and the Democrats will campaign on how "extreme" Republicans are).
This time, both plans backfired.
The Republican Study Committee proposed a "moderate/reasonable" bill to balance the budget in four years. That's four years longer than it should take, of course, but a lot less time than other plans (Paul Ryan's budget supposedly balances in ten years, and none of the Democratic plans balance at all, ever, period).
Most Democrats voted "present" in hopes of forcing the Republicans to pass the "moderate/reasonable" -- er, "extreme" -- bill. That didn't work; the bill didn't pass.
The Republicans, not having enough cover from Democrats to blame them for killing it, decided they'd rather kill it themselves than risk the slim possibility that it might ever get through the Senate and past the president.
104 Republicans voted to balance the budget in four years. 118 Republicans voted not to. QED, at least 53% of Republican US Representatives oppose balancing the budget any time in the near future, so much so that even if they can't shift the blame for not balancing the budget onto the Democrats, they'll still vote against balancing the budget.
And that 53% is a best-case scenario -- some who voted for the bill may have actually opposed it, but knew that it could be killed without a nay vote their constituents might notice.
Even counting the Democrats who did vote, only 15 more Republican votes would have passed the bill.