Reid's staff disputes this version of events. In their telling Reid and his aides pursued a range of options at both the staff-level, and at a principals level, through the weekend. Reid was willing to accept budget cuts in two phases, but would not agree to a short-term debt limit extension if it just meant replaying this fight all over again several months from now. Boehner wouldn't (or couldn't) bite. Reid left a Saturday evening meeting angry, said no short-term deal, and began contemplating the one-step approach, which leaked Sunday afternoon, and that he ultimately settled on Sunday night.
Republican and Democratic staff continued to pursue a two-step solution to the problem on Sunday, while Dem staff began worked separately on the one-step plan on their own. By Sunday evening, the two separate debt hikes remained a sticking point, and at a White House meeting last night, Reid presented Pelosi and President Obama both frameworks. All agreed that that the single-step process was the way to go -- really the only bright-line Dems have drawn in this entire debate -- and that's why things ended as they did late last night.
The conflicting narratives suggest there isn't a whole lot of good will left between the interested parties. But whether or not they feel they got tripped up by the Dems' decision, the big question now is whether Republicans will accept the offer on the grounds that it's, well, pretty much everything they've asked for. We'll learn more in the coming hours.