From reason:

Not everyone is convinced. In USA Today, the R Street Institute’s Anthony Marcum makes the case against term limits.

Although well-intentioned, term limits have a problem. Not only are they unconstitutional, but they will have the exact opposite result proponents wish for. More, term limits will ensure that court vacancies are inextricably tied to every presidential race and has the potential to create abrupt ideological shifts on the highest court, only increasing the political scrutiny. In other words, term limits will not lower the temperature around nominations, they will leave the country scorched.