Putting aside the question of whether congressional and senatorial term limits are a good idea, it can only happen through a constitutional amendment. It is unconstitutional for a state to impose any term limits on federally elected officials.
An amendment would require 2/3 of both houses to approve the amendment, which isn't going to happen, or a constitutional convention called by 2/3 of the state legislatures. And none of the Amendments to the constitution resulted from the latter.
But for those, who want term limits, the best answer is we already have them. The members of congress and senators are subject to election and reelection. If there is a problem with bad people in office getting reelected constantly, there is then a bigger problem with the people, who keep installing them in office.
If that is the case - why is there a need for term limits for the President? I think we should either have them for all, or not at all.
The XXII amendment limits the terms of the president. The difference is that the presidency is an executive office with considerable power vested in one person.
A senator or congressperson works in the legislative branch. Singularly his or her power is comparatively minor; its strength rests entirely in its body composing many people. As such, there is more of a need for term limits for the chief executive.
James Madison spoke out against term limits for congress in the Federalist Papers. Again, the people have the power of term limits in the ballots they cast.
