Fortunately for the Yankees, they had David Phelps instead.
It's crazy to think that Dempster, one of the most coveted pitchers at the non-waiver trade deadline, was destined to be outpitched by the Yankees' replacement for CC Sabathia. But that's only half the story of their 8-2 victory over the Rangers.
The other half involved the rebirth of Derek Lowe, who followed up Phelps' two-run effort over five innings with four scoreless of his own, retiring 12 of 14 to earn his first save since 2001.
For a Yankees team trying to cope with losing Sabathia for the second time in six weeks, this helped. A lot.
"I don't know how you can ask two guys to do any more than that," Joe Girardi said. "That's really stepping up."
But that's only the first step. Sabathia, who went on the DL with elbow inflammation, is scheduled to return Aug. 24 against the Indians. Of course, that's the best-case scenario.
Too often, what typically follows the diagnosis of "elbow inflammation" for a pitcher who has 2,500 innings on his resume is Tommy John surgery. If not immediately, then at some point in the not-too-distant future.
The Yankees are treading carefully with Sabathia, keeping their fingers crossed that he can rebound for a playoff run.
In the meantime, they'll lean on Phelps, use Lowe as a competent safety net and anxiously monitor the progress of Andy Pettitte, who is not expected back until mid-September, at the earliest. For one night, at least, this patchwork scheme worked beautifully.
"You can't replace him," Phelps said of Sabathia. "He's just been so valuable. I hope I can at least give a percentage of that. Just keep us in the game as much as I can."
Girardi believes Phelps can handle that responsibility. In four starts for the Yankees this season, Phelps has allowed five earned runs in 18 innings for a 2.50 ERA. Compare that to what Dempster has done for the Rangers. After owning a 2.25 ERA in 16 starts for the Cubs, Dempster has an 8.31 ERA in three starts for Texas, which slipped behind the Yankees for the AL's best record with Monday night's loss. In two of those starts, Dempster has been ripped for eight runs. With Chicago, Dempster allowed as many as eight runs only once in 52 starts.
It's been the reverse for Lowe, who had an 8.77 ERA in his final 10 starts for the Indians before they released him.
The Yankees aren't likely to use Lowe in a starting role unless the rotation springs another leak, and that's something they really can't afford at this point. But he does provide backup, which could turn out to be crucial with five-and-fly types Phelps and Freddy Garcia holding down important jobs for the immediate future.
"It couldn't have gone any better," Lowe said. "I'm not going to lie and say I'm not going to sleep with a smile tonight."
That goes double for Girardi and Brian Cashman. But how long can they continue to piece together the rotation in its current form?
"The last time, they responded pretty well," Girardi said. "When Andy and CC went down, this group did it before. They stepped up."
Sort of. The Yankees went 9-6 during that stretch but nearly doubled their division lead, from five games to nine.
Is that too much to ask the second time around? If Monday night was any indication, there's no need to worry just yet.