The Twins are winning right tonight, so they have a shot at being 42-47 going into the break. They have gone 22-11 since the beginning of June, salvaging a miserable season in the process. If they follow their 2nd half average since 2002 (and win out until the break), they would finish 84-78. That would be a remarkable turnaround for a team that was 12-27 and 17-37 at various points this season.
Unfortunately, that would probably not be quite enough to win the AL Central. Even in a weak division, the winner usually has over 84 wins. If they go 45-28, though, that would give them 87 wins (I'm assuming they'll sweep the White Sox, but they would need an even better 2nd half if they don't).
If the Indians or Tigers can win 90 games, it's going to be extremely difficult, if not impossible for the Twins to pull off another stunning comeback this season and make the playoffs. The Indians have shown enough flashes of brilliance this season that they probably should be able to win 90 games. The Tigers also have plenty of talent, but they have a history of falling off in the 2nd half.
The Twins were 7 games out on September 6, 2009 (26 games to go), and still ended up in the playoffs (with 87 wins). Considering their recent history in the 2nd half (and the fact that they finally have Joe Mauer back and hitting), the Twins do have a shot at the playoffs, although they'll need a lot of help from the Indians and Tigers.