"The House of Representatives . . . shall have the sole Power of Impeachment."
A lack of constitntional qualifications is a basis for impeachment and upon conviction, removal from office.
There isn't any other constitutional way to remove a healthy and living president from office, for any reason. Period.
The question in this case is whether Obama can “act as President”, or whether the 20th Amendment requires Joe Biden to “act as President until a President shall have qualified.”
The issue is to see who can Constitutionally carry out the duties of the President right now. That totally depends on whether Obama had “failed to qualify” by Jan 20, 2009. This isn’t about removing Obama, but whether he can Constitutionally be doing any of the things he’s been doing.