OK, after reading Greg Sargent's reporting, and tweets from Joe Lieberman saying that he and Susan Collins have a stand-alone bill and that Harry Reid has committed to bring it to the floor during this session (although, so far, we don't have confirmation about when that will happen compared to when the Senate will adjourn), I think I have a better guess about Reid's thinking -- and, more appropriately for this blog perhaps, a bit of speculation about what this process has told us about Congress in the present information age.
First, what's happening.
Again, this is guesswork based on the above information, but it seems that what's happening isn't that Reid is giving up on DADT repeal; he's giving up on the strategy of bundling it with the Defense Authorization bill. At this point, the problem is that he can't realistically take up the larger bill without allowing any amendments at all...that's just not done. And once it's opened at all to amendments, then he's convinced that determined Republican supporters of DADT could drag it out, even if cloture passes every time its needed.
On the other hand, a stand-alone repeal bill could be brought up and, with 60 determined votes, avoid any amendments at all, thus radically reducing the necessary floor time. (Actual floor time required would consist, if I have this right, on post-cloture time on a motion to proceed and then post-cloture time on a motion to bring the bill to a final vote; both motions would need time to ripen, but that doesn't tie up the Senate floor).
Now, whether the new plan will work depends on whether Harry Reid and the Democrats (and House Democrats) are willing to stick around and do it. That, we don't yet know. It may depend, too, on how quickly the tax bill and any other business can be finished. And perhaps Republicans will be able to throw up enough roadblocks to run out the clock, after all.
Meanwhile, the original advantages of bundling repeal with the Defense Authorization bill turned out to have been a flop, or at least half a flop. The idea behind it was always that marginal Senators would be afraid to vote "against the troops" and would therefore vote for the larger bill even if they didn't want to vote for DADT repeal -- and that other Senators who may have wanted DADT repeal but didn't want to vote for it would be spared a separate vote. Perhaps that's worked with some marginal Democrats (all Dems but Manchin voted yes today), but it certainly didn't work with Republicans.
And here's where I think this process is telling us something. Under current conditions, it sure seems to me that this particular kind of procedural trick is useless. No one can "sneak" a vote through. In particular, that's the case for partisan information flows. If GOP-aligned media sources said that Dick Lugar, or Scott Brown, or other Republican Senators were betraying their party by voting in favor of the Defense Authorization bill, then Republican activists in their states would hear about it and know about it, and it might well spark a primary challenge. Once upon a time, Members of Congress could cast these sorts of confusing votes and assume that the only person they had to worry about was the Washington correspondent(s) of their local paper(s). Now, those Washington correspondents are gone, but there's a whole internet (not to mention lots of paid lobbyists, think tankers, and others) watching everything, and transmitting the information relatively efficiently to party activists.
(For that matter, once upon a time Congress used "teller" votes rather than recorded votes in most cases, and unless the reporter happened to be in the untelevised chamber at the time there was no way of knowing how anyone voted).
Now, that doesn't mean that logrolling is no longer viable; there are still plenty of issues that no one is going to care about unless partisans get pumped up about them. But it does mean that for high-profile issues like DADT, it probably matters a whole lot less how they're packaged. We can't be sure; it's possible that bundling the two together did win the votes of some marginal Democrats -- who now, having voted for it, will presumably stay for it in stand-alone form. But odds are that the whole clever strategy was a full waste of time.