I'll be conservative and say none, but with a reasonably successful term Obama could win Missouri or Arizona. Any other state would be a bit of a stretch.
McCain won Arizona by roughly the same amount (about 9.5%) the usual difference for a favorite son -- about 10%. He won't be running in 2012, and it's hard to imagine any GOP nominee having any connection to Arizona. Romney or Huckabee would almost certainly have lost Arizona to Obama. To give some idea of how strong the effect is, look at how much better George McGovern did in South Dakota in the 1972 election than in politically-similar North Dakota: about 45% of the vote in SD as opposed to 36% in ND. The two states were within 3% of each other in 1976 (Ford 48% SD, 46% ND versus Carter). For a winner? Contrast Alabama, which Bill Clinton got about 43% of the vote, and Arkansas where Clinton won 53% of the vote in 1996. Arkansas and Alabama would seem to be fairly similar in demographics.
George W. Bush won Texas by a margin of 23% in 2008; John McCain, with no particular connection to Texas, won it by 11.7%. To be sure the GOP had a bad year in 2008 in contrast to 2004... but not
that bad. That McCain in 2008 won Arizona by the same amount that Dubya did in 2004 suggests that either
(1) McCain was an unusually-inept campaigner
(2) Dubya was a politician of unusual competence
(3) the Favorite Son effect is a myth, or
(4) Arizona and Texas have been changing in their demographics
... Obama was a far stronger campaigner than John Kerry and had a far better-organized campaign than Kerry, so that (1) and (2) are likely irrelevant; if anything, McCain would have crushed Kerry in 2004. The Favorite Son effect is genuine, so one needs to consider demographics. Mexican-American populations that strongly supported Obama everywhere have been growing quickly in both Texas and Arizona, and more significantly, Mexican-Americans of voting-age have been growing rapidly in both states. Add to this, both states are have fast-growing cities and suburbs, and urban America votes for high-priced government because it could not survive without it. Suburban America has been becoming more urban in character and less rural -- and less politically-conservative.
The population in Arizona is heavily concentrated in two counties: Maricopa (greater Phoenix -- McCain's political base) and Pima (greater Tucson). Texas has six cities with populations over 400,000 -- Houston, Dallas, San Antonio, El Paso, Austin, and Fort Worth -- and except for Fort Worth, their respective counties voted for Obama. Bigger cities imply larger support for Big Government.
Should Obama fare as well nationally in 2012 as he did in 2008, then he probably picks up Arizona; the GOP nominee will have no connection to Arizona. Obama would win Arizona by a thin margin -- probably by 1% to 3%. Texas? Obviously not unless things change dramatically.
Few people expect the political dynamics of 2012 to resemble those of 2008. There will be demographic shifts (larger Latino populations and bigger urban areas), there will be generational change (youth born between 1990 and 1994 are likely to vote heavily Democratic just as did those born between 1986 and 1990, the youngest voters of 2008), and of course there will be success or failure of Obama as President. Obama might not need much political success to flip Arizona; to flip Texas he will need considerable success.
So if I were to make a medium guess on Obama 2012, I would expect Obama to win Arizona by about 1%... and lose Texas by about 5% (urbanization and demographic shifts making the improvement). I would also expect Obama to find some of his double-digit margins of support in the Northeast, Midwest, and West Coast to erode... some... and much the same happen in some states that he lost by large margins. Call it reversion to the mean, and with about the same percentage of the popular vote that he got in 2008 he might pick up a state or two in the popular vote.
Note also that Obama got comparatively few electoral votes (365) for his margin of victory (53-46) which is about the same as for Bush 1988 (53-46, 488); Eisenhower 1952 (55-44, 442); and FDR 1944 (53-46, 432) in elections in which third parties did not figure important. That suggests political polarization far more severe than in a war that decided the fate of Western civilization, the complacent era of post-WWII era, or the Reagan-era consensus. Such polarization could erode (probably indicating general success), and even slight success could swing a few states to Obama.
But that's the small picture. The big picture remains to play -- and we have yet to see whether Obama is an unqualified success or an unqualified failure, or most likely somewhere between those polar opposites. Much must go wrong for Obama to lose one of the large states that he won by a double-digit margin (MI, PA)... and much must go right for him to pick off a state that he lost by a double-digit margin (TX, GA).