Any eligible citizen (all native born citizens but Presidents Obama, Clinton, and George W. Bush over the age of 35 can run). So, in theory, anybody who is eligible could still run.
Having said that, every state has laws governing getting on the ballot has "filing periods" -- one deadline for candidates who want to run as the nominee of "established parties" and one for candidates who want to run as nominees of "new parties" or as an independent. Both major parties rely on primaries and caucuses held in the first part of the election year to choose delegates to conventions that officially nominate that parties candidates. And most states use primaries to award their delegates. Assuming that Michelle Obama were to run and run as a Democrat, she would need to file before a given state's filing deadline to be on that state's primary ballot. At this point in time, no filing deadline has passed yet (the earliest will be in the latter part of this fall).
Given that the Democrats award delegates proportionately -- based on the results in each individual state/territory and congressional district-- it is hard to skip being on the ballot in any primary and still win a majority of the delegates. And enough states vote on March 3, that it is mathematically impossible to win a majority of delegates if you miss those states. And, even if a candidate is well known, there is still a need to recruit delegates and put a field operation in place to turn out voters (crucial as presidential primaries have about one-third the turnout of the general election).
Realistically, since the modern system for nominating candidates began (1976), no successful candidate has skipped both Iowa and New Hampshire. (Some have put forth minimal effort in one of these states in years in which a regional candidate was running, but they have still tried to finish near the top even if they weren't trying to win.)
Finally, the latest that a successful candidate has announced was Bill Clinton in 1992 who waited until August 1991, but that was something of an exception to the rule as the First Gulf War in January 1991 gave the first President Bush a momentary bump in the polls and somewhat froze presidential politics for several months. Every other successful candidate announced before May 1.
So, Michelle Obama, if she wanted to, legally could still get in the race, but getting in now -- especially after the first two debates -- is highly unlikely and would probably not lead to success.