In my opinin, the secretary of states should be the defendants in this lawsuit. My apologies, I am multitasking.. :-p
In what lawsuit? What infraction would this lawsuit allege? Remember, there is nothing in the constitution requiring any specific act to verify eligibility.
I think the only case anyone could possibly have would be to claim that Obama is, as a matter of fact, ineligible. That the he, or the states, or the congress didn't satisfy everyone, isn't going to work. Suspicion will not work.
I think it's the need for instant gratification. People want results now!, they don't want to do the work. Instead of looking for a judge to give you what you want, someone has to do the work of finding the proof of the birther suspcions. There's no jumping to the end.
Of course, since the birther suspicions don't have much merit in the first place, it's exceedingly unlikely that any such proof will be found. But that still doesn't give you a shortcut.