It seems counterproductive. Surely the number of people getting pissed off and unfollowing the account would be quite large compared to the amount of good it would actually do.

I guess the world is still learning the answers to questions like "How many times a day can you tweet before you piss people off?"

Oh, just one other thing:

He's trying to initiate social action

Well no, the political posturing is what's important here, not the question of whether some random jerk leaves a message at some random congressman's office. The point of the campaign is to try to claim credit when the eventual compromise comes through (or else to be able to blame Republicans for refusing to "compromise" when the negotiations fall through). As always in politics, what you're seen to be doing is far more important than what you're doing.

And remember that in politican speak, "We want a bipartisan compromise" always means "We want the other party to vote for our bill".