"The House isn't technically refusing to pass a budget, they have passed a budget, and the Senate disagreed. And of course the legislature has the power to modify previously-passed law. How else does one make new law without a discontinuous government?"

http://www.nytimes.com/2013/10/01/us/politics/congress-shutd...

As Senate Majority Leader Read said, “We will not go to conference with a gun to our heads,” demanding that the House accept the Senate’s six-week stopgap spending bill, which has no policy prescriptions, before negotiations begin.

You're right that in normal legislative maneuvering, it's entirely appropriate for each chamber to pass different bills and resolve the conflict in conference. But in this case the House is clearly using the risk of default as leverage to force the Senate and the Executive into accepting unrelated legislative matters. Given that the alternative could be economic chaos, and that debt ceiling resolutions are a regular occurrence, what the House is essentially demanding is new authority to overrule Senate prerogative in legislative negotiation.

That's the crux of this. The issue is not merely this event. Should it become the norm, the House will essentially have crafted out of whole cloth a new veto authority over all current and prior legislation based on Article I Section VII.

EDIT: Here is Jonathan Chait on the matter:

http://nymag.com/news/politics/nationalinterest/government-s...

"The standoff embroiling Washington represents far more than the specifics of the demands on the table, or even the prospect of economic calamity. It is an incipient constitutional crisis. Obama foolishly set the precedent in 2011 that he would let Congress jack him up for a debt-ceiling hike. He now has to crush the practice completely, lest it become ritualized. Obama not only must refuse to trade concessions for a debt-ceiling hike; he has to make it clear that he will endure default before he submits to ransom. To pay a ransom now, even a tiny one, would ensure an endless succession of debt-ceiling ransoms until, eventually, the two sides fail to agree on the correct size of the ransom and default follows."