From a strictly political point of view, the only way either party would be willing to tackle the issue would be to take Obama out of the equation. Neither the Supreme Court nor either party in Congress will directly address a sitting President's eligibility, especially this far into his term. They would have to "grandfather" Obama's eligibility before anyone would touch it.
Yes, the SCOTUS appropriately wants to avoid impacting the political process so far as possible. OTOH, one can see scenarios where the people, and, basically, the rule of law have no other means of remedy.
When Congress will not do its job in a transparent and accountable way, and the SCOTUS — again, appropriately — is very cautious about impacting the political process, there are times the country is going to get screwed royally.
I’m not saying the SCOTUS should not take an appropriate case. But the real answer to this is to get legislation passed that makes the process for evaluating whether a candidate is eligible to serve as president something that is NOT arbitrary and capricious, as it sometimes appears it is now.
IOW, a process that has a written STANDARD, set PROCEDURES, a process for REVIEW, and a REMEDY for failure to apply the standard and procedures in a reasonable way.