Auctions on eBay have a deadline and aggressive bidding occurs just before the auctions ends. This is called “sniping” (see this excellent paper for a discussion along with the study of many other interesting issues). One reason offered for this behavior is that bids might not come in as the auction ends so if your low bid gets in and my high bid does not, you win anyway (I seem to remember a paper by Al Roth along these lines). A similar effect arises in the debt limit negotiations.
Assume for now the deadline is August 2 – if the debt limit is not raised by then all hell breaks loose. If the House has a proposal on the table later today, this gives the Senate the change to reject it and table their own proposal. But if the House gets their proposal in on August 1, there is too little time left for the Senate to respond with their own bill. If they reject the House proposal, all hell breaks loose. And if the President vetoes the bill, all hell breaks loose. So, there is distinct advantage to the House from delaying the vote. Symmetrically, there is similar advantage to the Senate from delaying the vote. But if both delay the vote, there is also a huge risk that neither proposal makes it through either chamber because both Reid and Boehner are having hard time drumming up enough votes. So, as both parties delay the vote, there is a huge chance of hell breaking loose….
What if the August 2 deadline is not hard? Then, I think I need a model to sort things out but my intuition is that there is bigger incentive to accept an early agreement (after August 1)- if you reject it, there is chance your counter proposal does not make it through as all hell breaks loose because the government runs out of money. But if early agreements might be accepted, there is a bigger incentive to move early and get your bid in…..