However, Red Sox manager Terry Francona won't give in to that temptation. Win or lose on Monday, it will be veteran knuckleballer Tim Wakefield taking the ball the next night for Game 4.
"He's pitching," Francona said of Wakefield.
The decision is one the Red Sox have given a lot of thought to and they simply feel they have a better chance of winning the series by keeping the rotation as it is.
"You know what, I think what we're trying to do is set up our rotation so we can win a series," Francona said. "I think sometimes you get short-sighted if the need for panic arises, like perceived panic. If you lose a couple of games, everybody wants you to immediately change what you've set up. The reason we set it up like this is because we think it gives us our best chance to win a series."
Francona can understand the public sentiment of wanting to see Beckett pitch as many times as possible in the series. But it's his job to take a broader view of the situation.
"Doing something like [pitching Beckett in Game 4] may give you a chance to win a game, it may not, but it doesn't set up the rest of the series," Francona said. "We really value the rest that [Curt] Schilling can get, and Daisuke [Matsuzaka] also. It's not just one guy that it affects -- it affects three guys in the rotation."
Needing Gagne: Red Sox second baseman Dustin Pedroia knows how much Eric Gagne is struggling. He also knows that this is no time to give up on one of the most talented relief pitchers in baseball.
"We need him to win," said Pedroia. "A lot of you guys get down on him. We need him more than anybody. Big Papi, Manny -- we need Eric Gagne as much as anybody. We need him."
Gagne took the loss in Game 2, giving up a hit, a walk and two runs. Both of the runs Gagne gave up scored after he left the game amid a seven-run uprising by the Indians in the top of the 11th.
"We were actually going to let him face Trot [Nixon] if he had gotten [Asdrubal] Cabrera," said Francona. "But when he walked Cabrera, we decided to go to Javy [Lopez] even if they were going to hit for Trot with [Jason] Michaels, just because it's the 11th inning and it seemed like the right thing to do."
Gagne hasn't been effective in any of his three outings in this postseason, giving up four hits and three runs over 2 1/3 innings.
Red Sox don't dwell: As tough a loss as Game 2 was, the Red Sox didn't seem to have a problem brushing it aside. Perhaps some of that comes from the tone Francona sets.
"Well, there had better not be any carryover," Francona said. "That would be a horrible mistake on our part. That was one of the funnest games I've ever been a part of until the very end, and then it rapidly became not a lot of fun. We lost in kind of an ugly fashion at the end. ... I think we already did bounce back. I think the bounce back will feel better when we have a little sleep. But as far as dragging in the clubhouse, that won't happen. It shouldn't and it won't and there's really no reason for it to happen."
The players seemed to have a similar stance. It wasn't as if anyone expected the Indians to be anything less than a highly competitive opponent.
"They had the same record as us during the year," said Pedroia. "They're a good baseball team. They're going to come out and play well every day. We have to try and beat them."
Many players optioned out of workout: Given that it was an optional workout and that the Red Sox didn't get to Cleveland until the wee hours of the morning, it was not surprising that only eight players on the active roster worked out at Jacobs Field on Sunday.
The active players who did take the field were Jacoby Ellsbury, Doug Mirabelli, Jason Varitek, Beckett, Matsuzaka, Pedroia, Tim Wakefield and Bobby Kielty.
Bugged out: Considering the bugs that invaded Jacobs Field during Game 2 of the Indians-Yankees Division Series, it wasn't surprising that media members would ask the Red Sox about it entering the Cleveland portion of this ALCS.
However, Francona didn't quite know how to answer it.
"I don't know what to say," Francona said. "You know what, it's kind of like rain. You handle it. If it rains, you handle it. If it snows, you handle it. If it's cold, you handle it. I guess if there's bugs, you get bug spray."
Speaking of which, Matsuzaka confirmed he did pack some for Game 3.
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.