They can argue for the Supreme Court to "step in" all they want, but only the Congress has the power to "remove" a setting President.
The SCUTUS -- or another court -- could make a ruling that would be, ahem, "embarrassing" to Obama... thus turning up the pressure in such a way that his power would be neutered, at best, with a good chance of him stepping down of his own accord.
I have great respect for the constitutional principle of separation of powers of the three branches of government.
One branch of government does not have the authority to usurp the powers delegated -- by the Constitution -- to another branch of government.
It may be worth noting that President Nixon was never impeached: but under mounting public pressure he was "forced" to resign.
The idea is to get him and his anti-American cabal out of The White House without too much disruption to our republic.
You are correct in that we should not want to depose a would be dictator at the expense of finding ourselves living under a judicial oligarchy.
Frankly, I don't think he has another term in him.
Let us pray!
STE=Q
IIRC Honduras had a similar problem with their President??
Wasn't it the MILITARY who had to remove and re-locate him, hmmmm???