All these people talking conspiracies about Obama wanting a third term and he will get it by martial law... I'm just like:

That brings up the question of is a former two-termed President even allowed to be in a position where he could become President again.

That point is a bit harder to answer than you'd think...
https://www.quora.com/Could-Barack-Obama-be-elected-Vice-President-in-2016

Good question. I had a similar discussion with my son the other day. The Republicans seem to be bent on finding a way to deny Trump the nomination. If they are successful and there is no republican nominee all Obama would have to do would be to give the DOJ permission to indict Hillary on her crimes and take her off the ticket too. With no nominees from either party Obama could make a claim for a 3rd term.

There's still the third-party candidates though.

Yeah, even after third party candidates there's independent candidates. And there's no way that if that happened no one else would run. Plus, I honestly don't think Obama wants another term, and the democrats don't want him to have another either. They might still like him more than Hillary... but he has lost popularity. He's no longer their favorite, people have already moved on to listening to whatever Hillary or Bernie says and believing whatever they say.

That is not true. Obama is constitutionally barred from being elected again. There does not seem to be a clear prohibition on his being the president again, but he cannot be elected to the post. The Electoral College must meet, and it must either elect someone or refer the matter to the House of Representatives. Political parties have no constitutional standing in the process.

I'll admit, it is an interesting idea.