My hunch is that Senator Clinton already knew (for Senator Obama had already taped an interview with Fox) that her rival had refused further debates when she fired off her audacious challenge to a Lincoln-Douglas style debate sometime before the Indiana primary. She understood that this meant no moderators, which was supposed to make Obama happy, but did she understand the other rules? Is she actually prepared to speak extemporaneously for more than an hour? Does she realize that, for the Lincoln-Douglas format to be fair, there must be at least two debates, so that each candidate has a turn as the first speaker and gets to rebut the other's reply? Even given Obama's reputation as an orator, can you imagine either of them making it through a true L-D style debate without serious "gaffes" and misstatements? But as I said, I suspect these points are moot because Clinton didn't expect Obama to accept the challenge.
Obama has most likely demurred because, even without moderators of suspect loyalties, he knows that as long as his opponent remains the same any debate with her will be about "electability" rather than the issues of the day. The Illinois senator has made clear that he's sick and tired of these "distractions." I addressed the point already a few days ago, but to repeat: electability is a valid issue when a party chooses its candidate, but in a democratic party with primary elections voters have just as much right to consider who'd make the better President as they have an obligation to consider electability. If electability is the primary consideration (pun unintended but probably subconscious) for party leaders, they should never have let the nomination process out of the smoke-filled rooms. For his part, Obama has the right to assert that policies determine electability more than distractions, and Clinton has an equal right to argue otherwise. But I don't think any group of Democrats in Indiana wants to be in a room for three hours hearing that particular debate, and I know the candidates don't need to be in that room to debate the point further.
If Clinton really believes that the 1858 format has virtues, the first thing she should do if nominated is issue the same challenge to McCain. That should be even less of a risk than her current ploy, because the Republican would most likely have even less desire to pull such a stunt than Obama does, for fairly obvious reasons.