These players should be fairly easy to obtain. To make the list they had to be signed as minor league free agents this past offseason. There are several players who could be useful stopgaps. We'll start with a name well known to many Twins fans.
Dan Johnson - 1B - .301/.470/.585 for Charlotte. I doubt the White Sox are going to need him. Bring the hometown kid back and let him get some playing time. I was on board with signing Johnson this offseason and keeping Parmelee in AAA.
Scott Moore - 3B - .306/.414/.593 for Oklahoma City. If he can field at 3B he's a steal as the lefthanded half of a platoon.
Luis Valbuena - 2B - .327/.398/.478 for Iowa. Has major league experience. Isn't a terrible fielder, would free up Casilla to play a utility role.
Steve Pearce - 1B - .331/.423/.579 for Scranton Wilkes-Barre. This guy was actually signed by the Twins this offseason and released in March. In hindsight this looks like a mistake. He's probably not going to get called up by the Yankees either.
Bobby Scales - UT - .339/.459/.486 for Buffalo. Has played a little in the majors and in Japan. A switch hitter, he could be worth giving a shot at 3B in a platoon with Valencia.
Hector Gimenez - C - .252/.317/.409 for Charlotte. Same as Navarro but without the pedigree.
Omar Quintanilla - SS - .289/.358/.512 for Buffalo. If they want Carroll at 3B they could use Quintanilla as a utility player.
Valentino Pascucci - 1B - .285/.368/.504 for Buffalo. A favorite of mine since he played for the Rochester Honkers. Can still hit left handed pitchers.
Aaron Cook - RHP - 33.1IP 13K 11B 1.89ERA
Justin Germano - RHP - 45.1IP 28K 5BB 1.99ERA
Dana Eveland - LHP - 36.2IP 19K 6BB 2.21ERA
Zach Duke - LHP - 42IP 27K 10BB 3.43ERA
Brett Tomko - RHP - 38IP 32K 18BB 3.55ERA
Garrett Olson - LHP - 42.2IP 44K, 23BB, 3.59ERA
Brandon Duckworth - 43.1IP 39K 14BB 3.95ERA
Jeff Francis - LHP - 49.2IP 47K 12BB 4.17ERA
Zach Jackson - LHP - 43IP 28K 12BB 4.19ERA
Compared with what we're getting in the rotation, any of these guys might help. I would be especially interested in Germano, Francis and Duke.