The chief justice of the SCOTUS is involved, as the presiding officer, in an impeachment trial, anyways.
If the SCOTUS were to review this, I'd bet they'd refer the issue to the Congress to investigate anyway.
Unfortunately, it'd die a quick death with the current makeup.
If Congress choose that route, they would befell a quick death in 2010. The drumbeat to remove Obama would be overwhelming. Congressional rats vs. Obama presidentency?
The Rats in Congress would throw him under the bus.
I don’t think so. If SCOTUS rules that Obama is ineligible, then it goes to Biden. I don’t think Congress gets any say in it.