The problem is proving it. If they cannot prove it, they cannot take it on. Believing it is not enough. Have you tried arguing this point with someone who doesn’t think it’s true? Did you win them over? I never have. And usually the argument ends with a “crazy birther” accusation. I don’t think that the republicans can afford to be stereotyped that way right now. remember what happened to Lou Dobbs? Glenn Beck? Hannity? They all were forced to drop this. Do you really think that the politicians would fare any better?
There are two issues, one of which is only marginally related to the Birth Certificate. The BC issue is to determine if he is a citizen at all, or possibly a naturalized one. The other issue lies in the citizenship, or lack thereof, of his father. The BC would be legal proof of who his father was, but otherwise it could contain exactly what was on the image of the CoLB, and he still might not be a natural born citizen. There's really nothing to "prove", except in a technical legalistic sense. What is needed is a "determination". Much like the case of "Wong Kim Ark", where both sides agreed on the facts, but disagreed on the law (including the supreme law).
But it takes a court, including appeals courts and ultimately the Supreme Court to make that "determination". If no court will even examine the issue, declaring it "political" or that individuals have no "standing" to have the Constitution enforces, then the Constitutional meaning will not be defined, and the Constitution will not be enforced.
The BC issue is just easier to understand, no confusion between "(native born) citizen" and "natural born citizen" exists if he was not a citizen at birth at all or was but by statute, which means under Congress power to define an uniform rule of naturalization.