But that doesn't preclude SCOTUS ruling on the matter. See Marbury v. Madison, where, after much argument, the Court concluded it was powerless to grant the relief requested. Or see cases where the Court delineates the "political question" boundary, and refuses to render an order. It could take up eligibility, if it wanted to, and thought the issue was more important than the cases it does decide to take up.
Ruling on what?
If Obama is the president, which to most people is obvious, then he is the Commander in Chief and can act as such. That's not what I say, that's what the Constitution says.
If Obama is not the president, then no one has anything to complain about. Soldiers still have to do what they're told by their commanding officers.
You just can't ignore the Constitution. Obama is the president, even if he shouldn't be the president. As the president, there is only one way to remove him under the constitution - impeachment. Until he is no longer president, he is the Commander in Chief.
You want the Chief Justice, who administered the oath of office, to inquire as to whether Obama should be president? Maybe he should first inquire about whether Bush was a proper president because, if not, then the Chief Justice isn't a legitimate Chief Justice. And, how about the qualifications of every Senator who voted to confirm the Chief Justice?
There is a remedy here. Call and write Boehner!