Turning out an extra few percent can be the difference between winning and losing in swing states, a reality Karl Rove exploited in 2004 by papering the nation with anti-gay marriage initiatives.
Grim ably lays out the case for the prosecution: pot initiatives might turn out Democrats who otherwise wouldn't vote, helping Democrats up and down the ticket. But he doesn't cite any witnesses for the defense, which I did in this post. Important takeaway: Political scientists disagree about whether Rove's initiatives helped Republicans. That's because ballot initiatives turn out opponents as well as supporters, which mitigates their effect.
And to get even deeper, what success Rove's initiatives did have was greatly facilitated by evangelical ministers, who organized their flocks in support of the measures and got them to the polls. As pointed out in this post, it's not clear who would fill that organizing role when it comes to pot initiatives. Dealers?
Anyway, Grim knows this subject better than anybody, as his recent book on American drug culture (which covers the legalization movement) will attest.