Liberty and Freedom
He has introduced legislation every session since 1997. Obama wasn't president then, was he? How about these attempts?
"Attempts to repeal the 22nd Amendment date at least to 1986, when Rep. Guy Vander Jagt (R-MI) proposed legislation in the House that would allow President Ronald Reagan to seek a third term. Rep. Vander Jagt reintroduced legislation to remove the term limits on the presidency in 1987, 1989 and 1991, as did a number of Congressmen throughout the 1990s. Corresponding resolutions were proposed in the Senate by Sen. Harry Reid (D-NV) in 1989 and by Sen. Mitch McConnell (R-KY) in 1995.
You should at least read the links you reference.