In my understanding yes, goes to the house. And your right, no bill may very well be better than what's there because it won't be honored anyway. Is there a chance the republicans will say no at this late hour? If they do you can be certain all will blame them for whatever fallout comes...both here and internationally.
I disagree about blame. Of course, the usual suspects—domestic and international—will whine their usual talking points.
But I believe a majority of American voters see the Senate budget bill for what it is—business as usual. These same voters are demanding that there be no debt ceiling increase, no tax increases, immediant and significant spending cuts and an enforceable balanced budget requirement.
Those elements are absolutely essential to fixing America. Failing to do what you know is right because of some real or imagined blame game is an act of cowerdice. A person who discards his/her principles for expediency is obviously not principled in the first place.