Did Tea Party Rallies Add 5 Million Republican Votes in 2010?

According to this AEI study they did.

The researchers conclude that having a Tea Party protest on Tax Day, April 15, in 2009 increased the number of Republican votes in that area for the 2010 midterm elections and caused their representatives to vote more conservatively.

In fact, they estimate that the protests led to an additional:
25,000 to 46,000 local Tea Party organizers
170,000 to 310,000 protesters on Tax Day 2010
$840,000 to $1.54 million in donations to Our Country Deserves Better PAC
3.2 to 5.8 million votes in the 2010 House elections