Don't believe the hype. There might be 66 guys in Twins spring training, but they aren't really competing for roster spots. In fact, there may not be a single roster spot to compete for.
How come? Because of "options." Options are a MLB administrative rule that limits how long a team can keep a player on their 40-man roster but keep them in the minors. Basically, they have three years before they need to commit to bringing that player to the majors. For a little more on it, check out this entry, where I compared it to the amount of time before you move from dating to married.
If a player doesn't have "options" left, they cannot be sent to the minors without being offered to every other major league team. So a team risks losing that player, and that isn't a risk the Twins are usually anxious to take. Thus, a player without options almost always has the inside track to make it to Opening Day. And when you look over the 25 spots the Twins have available, player without options look like they're going to gobble up most of the open spots. Let's run through them.
The Twins entered spring training with their lineup and rotation pretty set, which (barring any injuries) takes care of 14 of the 25 spots on the roster
C - Joe Mauer
1B - Justin Morneau
2B - Alexi Casilla
SS - Jamey Carroll
3B - Danny Valencia
DH - Ryan Doumit
RF - Josh Willingham
CF - Denard Span
LF - Ben Revere
Rotation - Carl Pavano, Scott Baker, Francisco Liriano, Nick Blackburn & Jason Marquis
That leaves 11 spots, which probably includes four guys off the bench and seven guys in the bullpen. Here are heavy favorites for each of them:

  • Drew Butera is likely the backup catcher unless the Twins are really enamored with newly acquired JR Towles.
  • Trevor Plouffe and Luke Hughes are both out of options, so they're almost locks to be on the bench.
  • The fourth spot might be the only open spot, but the obvious option is Tsuyoshi Nishioka, who the Twins will be paying $3M whether he plays in the majors or minors.

And there are similar roster crunches in the bullpen. Four of the seven spots will likely go to Matt Capps, Glen Perkins, Joel Zumaya and Brian Duensing, all of whom are slotted for late-inning roles. And the other three spots? It turns out there are three relievers without options:

  • Anthony Swarzak is out of options, is right-handed and did a nice job in the swingman role last year. It seems obvious that he would make it.
  • Jeff Gray is a right-handed reliever who has pitched for several team the last couple of years. The Twins picked him up this offseason off of waivers because he was out of options. The Twins want at least one more right-hander in the bullpen, so he looks like a front-runner.
  • Finally, Matt Maloney is a left-hander that the Twins also picked up this offseason because he was also out of options. He has mostly worked as a starter, but so did Perkins before the Twins moved him to the bullpen. And a third left-handed reliever might make sense given that Perkins won't be used situationally.

Suddenly there are 0 spots left and another 41 guys in camp.