The Republicans believe that suing Obama will excite and turn out their base voters, and they're betting that this benefit will be larger than any political blowback. Whether they're right in this political calculation or not remains to be seen. But what is undeniable is that, so far, this lawsuit is nothing short of laughable.
Boehner has gone from confidently touting his and his fellow House Republicans' upcoming leadership on the issue of immigration, to now doing nothing more than groveling for Obama to solve the problem using his executive authority -- which is an ironic enough stance for a Republican to take, these days.
Poor Hillary? I don't think so. I think she's perhaps a little surprised at which particular aspect of her life is now being attacked (if she had a cartoon thought bubble over her head right now, it might read: "This is all you got? Really?!?"), but I don't think she's surprised the attacks have started.
The message this sends to other Republicans in Congress (both House and Senate) is that this can happen to anyone. The fear this is going to create may become all-encompassing in the House, and possibly even the Senate (if Republicans win control of the chamber this November). The Tea Party sword hanging over their heads is now plain to see.
Obama has gained back all the ground he had lost and then some (well, "and then a little bit more" would be more accurate...). He still hasn't quite made it back to where his poll numbers were before the Obamacare website rollout, but if the trendlines continue in May, he is at least within reach of this goal for the first time since October.
Congress is now doing what it normally does, in an election year. This is not intended to sound cynical, as I actually think it is a good thing for a divided Congress to stand up for its divided beliefs -- even while knowing that almost none of the bills it now votes on have a prayer of becoming law before the election.