Boehner abruptly announced his resignation last Friday, effective Oct. 30. But some GOP presidential candidates, conservative groups and congressional Republicans are also making McConnell a primary target.
As with Boehner, they accuse the Kentucky Republican of backing away from fights with President Barack Obama. That's despite his mathematical hurdle of having just 54 GOP Senate votes, short of the necessary 60 to end Senate Democratic delaying tactics, or the 67 to override Obama vetoes.
McConnell seems to have strong support among Republican senators. No. 3 Senate GOP leader John Thune of South Dakota says voters should aim their frustration at Obama.