A House bill would have embraced the sequester, deep automatic budget cuts designed to shrink the federal government. A Senate bill would have ended it, restoring billions of dollars for housing, roads and bridges. This week, congressional Republicans tacitly rejected both approaches to next year's budget, leaving frustrated lawmakers wondering how they will manage to keep the government open past September, much less resolve a broader conflict over the rising national debt.

As Congress prepared to leave town for a five-week summer break, the prospects for progress on any front in the endless Washington budget war appeared excruciatingly dim. Without an agreement to deal with the sequester and fund federal agencies in fiscal 2014, the government will shut down Oct. 1 — barely three weeks after lawmakers return to town. A few weeks after that, the Treasury will face the risk of default unless Congress can agree to raise the $16.7 trillion federal debt limit.

Leaders of both parties say they want to avoid those outcomes, either of which could seriously damage the sluggish economic recovery. But Republicans have so far refused to open official negotiations with Democrats, either over a budget blueprint for 2014 or over specific spending bills such as a $54 billion transportation and housing measure that Senate Republicans torpedoed Thursday.