A Senate leadership aide says McConnell hasn't taken Reid up on that offer yet. Even if he does, Democrats are counting on Republicans to maximize procedural delays, so have settled on the following process.
Whether or not Republicans ask Reid to tweak his bill or not, he will file cloture on his plan (or perhaps a slightly amended version) by midnight tonight.
Senate rules require Reid to allow one full day, and one hour, before he can hold the first test vote on the plan -- a cloture vote on the motion to proceed. He would thus call the Senate into session at 12:01 a.m. Sunday morning, and hold the vote at 1 a.m. If he gets 60 votes for the plan, he has to wait 30 hours before he can hold the next test vote -- to end debate on the bill. That 60-threshold vote would happen at about 7 a.m. Monday. If that works, he has to wait another 30 hours, before finally passing his bill in an up-or-down vote Tuesday at about 1 p.m.
Then it would be in the House's hands, where the question is: Can the extremely weakened Speaker John Boehner (R-OH) muster enough GOP votes for Reid's plan to pass it on a bipartisan basis? They'd have until just after midnight on Wednesday, when Treasury believes they'll run out of borrowing authority.
This process could be curtailed a bit. Boehner's bill should pass sometime Friday, and he can send it directly to Reid. It's a non-starter in the Senate, and Reid would demonstrate that with a quick vote to table it. But he can use it as a privileged vehicle to avoid the first test vote on the motion to proceed. That would take 30 hours off the clock -- but some Republicans would like to see Boehner withhold his bill, to force Reid to jump through all the hoops. Either contingency requires everything to happen precisely as planned -- and we're still looking at coming down to the wire.