The court cannot remove the President. <-— That’s a big fat period. Article 2 section 4 USCON.
Congress certified Obama’s eligibility de facto by certifying the election. each State’s Secretary of state certified Obama eligible de facto by putting him on the ballot. They are the arbiters of eligibility, not the Judicial Branch and certainly not either you or I.
You’re still not getting it. The court has the power to resolve controversies that arise under the Constitution. Eligibility certainly falls with the scope of such a controversy. This isn’t the same as impeachment. The stuff about Congress certifying the electoral vote does NOT resolve whether or not Obama meets Article II eligibility. Second, Congress is not given a specified power to be the so-called “arbiters of eligibility.” It would be a conflict of interest because a partisan Congress can simply ignore the issue (which is what has happened anyway). It still does NOT take away the court’s Constitutional power to resolve controversies that arise under the Constitution. A de facto officer can be removed for being ineligible. It’s not an impeachment but more of an annulment.