What would be the consequences? Would he be removed and if so by whom?
No. It’s too late. About all it might do, is prevent him from another term
The Constitution says that only Joe Biden can have the presidential powers, since Obama failed to qualify by Jan 20, 2009.
Anything that Obama has done using the presidential powers can - and should - be contested. That would include if he vetoes the repeal of healthcare reform (and hopefully a bunch of other unconstitutional crap) that the Republican Congress will pass.
This issue is far, far from being over. The dems are putting everything they’ve fought for on the line by keeping somebody who is documentably forbidden from having the presidential powers instead of letting Joe Biden do what is granted him in the Constitution. If they insist on having a fake in the office they will end up having NOBODY in the office from a legal perspective. Laws can be passed without a President’s signature, but only a President can veto. When we get a Republican Congress they will not be able to afford having no valid President - because it means nothing can be vetoed.
If we clean house in the elections, the fun can begin in earnest. We need to let our leaders know that - and know that both we and the law are on their side.