Along with Begich, Sens. Mark Pryor in Arkansas and Mary Landrieu in Louisiana each accepted money from the Koch Industries PAC in recent years. Blasting them now—all three are battleground races this year—risks making the incumbent look like a hypocrite.

And in Georgia, where Democrats have high hopes that Michelle Nunn can pull off an unexpected victory despite the hostile territory, the party must grapple with the presence of the Koch-owned Georgia-Pacific. The company, which makes a variety of products, employs thousands of people in the Peach State. Republicans have already signaled that if Nunn’s campaign attacks the Koch brothers, they’ll be ready to hit back by suggesting she’s threatening the business interest of her home state.

The strategy isn’t all downside for Democrats: Although most citizens may not know who the Kochs are, liberal activists certainly do—including the wealthy ones, from whom the Democrats are desperately trying to coax the kind of large donations that will let them push back more forcefully in TV ads. And the Kochs do complicate the GOP’s own political efforts, too, as when their company closed down a small plant in Alaska. It wasn’t a game-changer for the Alaska race, but it did allow Democrats to blast the GOP field’s ties to the brothers.