Their won't be any government shutdown or default this year, but that is not due to Republican cooperation or compromise in the House -- just the opposite. The House Republicans have been unable to agree on anything.
After passing a budget earlier this year, the Republicans assured their base voters that they would gain some concessions in the debt ceiling fight. They felt sure they could threaten to make the government default, and the president would give in and give them some more budget cuts -- and they could go home to their voters as heroes. That didn't happen.
The president, buoyed by his electoral victory in 2012, absolutely refused to compromise on the debt ceiling issue. He said he would settle for nothing less than a "clean" debt ceiling bill. Perhaps even more important, the House Republicans couldn't agree on what to demand for their vote to raise the debt ceiling. They argued for months about several possible demands, but came up with nothing they could all support.
For a while Speaker Boehner hoped they could at least pose as friends of veterans and agree to reinstate the veterans benefits they cut in the budget agreement, but they couldn't even agree on that (with those on the far-right refusing to restore those benefits, regardless of how unpopular the cuts were with the general public).
Finally, it became obvious to Speaker Boehner that the House GOP caucus would not be able to agree on any demand, so he opted to save the party's reputation and allow a vote on a clean debt ceiling bill. He knew that the last threat to default (and the government shutdown) severely hurt the party's image, and he wasn't about to let that happen again in this election year.
The House then approved raising the debt ceiling until well after the coming election (about March of next year) on a 221 to 201 vote. Those voted to raise the debt ceiling were 193 Democrats and 28 Republicans, while those voting against that were 199 Republicans and 2 Democrats (Barrow of Georgia and Matheson of Utah).
The Senate also passed the clean debt ceiling bill -- on a straight party line vote (55 to 43). Those voting for the bill were 53 Democrats and 2 Independents, while all 43 of those voting against the bill were Republicans. Like their counterparts in the House, the Senate Republicans wanted to be able to tell their base voters they opposed the raising of the debt ceiling -- but they didn't have the political courage to follow through by filibustering the bill and threatening a default.
The Republicans won't admit it, but they blinked again. The president and the congressional Democrats stood firm -- and they won.