One of the potential side effects of Eric Cantor's loss in the Republican primary on Tuesday is that it marginally increases the still very small chance that the House Republicans will vote to impeach Barack Obama.
The mechanism by which this might occur is complicated: With Cantor gone, there is no clear heir apparent to John Boehner as speaker of the House. This increases the chance that someone friendly to the Tea Party will be the next speaker, or at the very least someone who owes their speakership to Tea Party radicals.
There have long been a number of House radicals that would support an Obama impeachment for almost any reason, but their number is very small. There is a somewhat larger group of House members that are looking for evidence of a scandal that would allow them to vote for impeachment.
Even so, at present, the rest of the House membership thinks that impeachment is a stupid idea that will ultimately hurt the party. No impeachment vote will occur unless something changes that convinces most of the people in this third group that impeachment is a good idea. (Obviously it is very unlikely that a Democratic-controlled Senate would vote to convict Obama. However, the Democrats may lose control of the Senate in 2014. And even if the Senate fails to convict, impeachment might be good politics if it helped Republican candidates get reelected in 2016, or if there was a plausible reason to think that it would hijack and seriously weaken the Democrats' political agenda between now and 2016.)
The most likely reason for these Republicans to change their minds about impeachment is scandal-- by which I mean activities that are both very unpopular and bear a serious suspicion of illegality. If Republicans have not yet found such an impeachment-worthy scandal, it is not for lack of trying. Republicans have tested a number of different such wannabes (Benghazi, IRS, Solyndra, Fast and Furious, Veterans Administration, the Bergdahl prisoner exchange, Libya, presidential executive orders, unilateral changes in Obamacare, etc.), but none of them has yet taken hold with the public and with Republican politicians in a way that makes impeachment appear politically advantageous to most House Republicans. To be sure, the Republican base matters more than the public as a whole. Even if impeachment is unpopular generally, Republicans might support it if there is sufficient pressure from the Republican base demanding it.
But the way that the Republican base thinks about impeachment depends in part on what the Republican political leadership in the House does with the investigative and messaging resources at its disposal. A Republican House led by Tea Party stalwarts is more likely to use the resources of government in ways that will make impeachment more popular among the base, and more thinkable among the rank and file of the House.
Thus, replacing Speaker Boehner with a Tea Party Republican, or a speaker heavily in debt to the Tea Party, changes the calculus of political considerations. It increases the chances that the speaker will make decisions that make it easier for House radicals to drum up support for impeachment. Note that even before Cantor's loss, Speaker Boehner, accommodating pressure from his party's radicals, had finally agreed to form a select committee to hold hearings on Benghazi. The Bergdhal prisoner exchange will likely lead to more investigations, and, in the next several months, other accusations of illegality may emerge. Who leads the House Republicans will matter greatly in how these controversial issues are handled.
Although the chances of impeachment are very small, they got just a bit larger with Cantor's loss.