Rodriguez has been on the disabled list with a strained right quadriceps since April 20, and he is expected to play in a couple of Minor League games next week if he is cleared after undergoing an MRI exam.
Posada landed on the DL on April 28 with right rotator cuff tendinitis. The Yankees hope he'll be able to start some light throwing in Tampa.
"I don't think you ever try to learn to live with it," Girardi said of his sputtering offense. "We've run into some pretty good pitching. [Fausto] Carmona is the type of pitcher who can shut you down, and so is [Cliff] Lee. But I believe our offense is better than what it has shown, and it is frustrating for all of us.
"The only thing you can do is try to grind it out and hope it turns today."
Girardi said he's going to be very careful with Rodriguez. There will be no race to get the powerful offensive player back into the lineup until he is ready. The manager said it's a near imperative that the third baseman plays in a couple of games before being activated.
"I think he has to because we have to make sure, too," Girardi said. "Everyone knows Alex is a routine guy, and I think he'd be more comfortable trying to play in a couple of games."
Girardi ruled out bringing Rodriguez back to serve as a designated hitter before the infielder is ready to play at third base.
"The problem with that is you still have to make the quick starts out of the box," Girardi said. "Sometimes those can be the worst ones as opposed to the field. So we have to make sure he's 100 percent. And to me, 100 percent is that he can play his position as well. I get more worried about quick starts out of the box than anything."
In fairness to New York's offense, Girardi said the pitching staff is as much to blame for the streaky nature of the team's play as is the offense. In four of the five losses this homestand, the opposition scored five or more runs. However, the offense was also held to four or fewer runs five times.
"I think some of the inconsistencies we've had with some of our starts, our pitching starts, led to the streaks we've been involved in," Girardi said. "To me, it all starts with starting pitching. You have to have starting pitching to compete on a daily basis. Our starting pitching the past week has been really good, and we need to continue to do that."