UPDATE: Timing of Senate vote on debt ceiling

Unless Republicans drop their opposition to Reid’s plan for raising the debt ceiling, Senate rules would make it impossible for the Senate to vote on Reid’s proposal before Sunday, two days before default.  Even that might not be possible if a single Senator objects.  Good news is that Treasury may have some breathing room.

Senate rules make vote in Senate before Sunday unlikely; vote could even come later

Michael McAuliff got this summary of Senate rules from a senate aide working on the planning for a vote:

In order to vote to end debate on a measure, a senator must file for cloture, and the rules require an "intervening day" for the request to "ripen." In this case, the Senate is planning to use an existing measure already on the floor as a vehicle and attach the debt bill as an amendment.

Reid is expected to file for cloture on that motion to proceed to the "substitute amendment" Wednesday, a plan he's expected to detail at a press conference Wednesday.

With an intervening day on Thursday, the Senate could have its first cloture vote -- with a 60-vote threshold to end debate on the motion to proceed -- on Friday.

Senate rules also require 30 hours between each step in the voting process, unless senators unanimously agree to waive the time. That delay would set up an up or down, majority vote on the amendment for Saturday.

If the debt amendment passes, the underlying vehicle would then also have to be passed 30 hours later, also by a simple majority, putting that vote somewhere later on Sunday.

See: http://www.huffingtonpost.com/2011/07/27/senate-debt-timeline-no-margin-error-default_n_910666.html

It may be possible to extend the deadline for default past next Tuesday

There is a report that Treasury might have found enough money to extend the deadline by a few days.  Huffington Post got this estimate of the true deadline from Barclays Captial:  

P]revious projections showed the Treasury running out of money on the morning of Wednesday, August 3. On that day, it was predicted, the Treasury would need to spend $32 billion, including $22 billion in Social Security payments -- and it was only projected to have $30 billion at its disposal.

That projection was made on July 13. But since then, the researchers say, the Treasury has taken in about $14 billion more than expected, and paid out about $1 billion less than expected. Hence, the deadline date might actually be August 10, a week later than previously believed.

Source: http://www.huffingtonpost.com/2011/07/22/debt-ceiling-august-10_n_907480.html