Its been tried.
The Democrats first sued their constituents in 1994 over the issue when Speaker of the House Tom Foley went to court against the citizens of Washington State for term limiting him. The Democrats had been fighting term limits for years until they were beaten by the voters. A friendly Federal judge was procured and the term limits laws passed by the people of Washington overturned.
Federal Judge Strikes Down Law Limiting the Terms of Lawmakers
With a fresh victory over American citizens under their belt the Democrats moved in 1995 to their enforcement arm, the Supreme Court, to overturn all state term limit laws. In
USTL v Thornton the Democrats succeeded once again in court where they had failed legislatively and democratically. They crushed their citizens and had term limits declared unconstitutional once and for all. (sound familiar?)
Ginsberg, Souter, Breyer, Kennedy and Stevens decided for the Democrats against the American people in this case at the Supreme Court.
Renquist, OConner, Scalia, and Thomas sided with the people but were outvoted.
Same song different verse. They are still doing it today.
So a constitutional amendment would be the only way to go. Not a chance in hell. The Democrats didn't waste all that effort suing their own constituents just to give up power now. And Nancy Pelosi is thinking that if she made herself a multimillionaire on a government salary in 32 years in Congress just think what she could do with another few decades.
