I'm not aware of particular proposals that have a lot of legs, but in one 2012 poll
Just one in eight Americans said the justices decided cases based only on legal analysis. [...]
The public is skeptical about life tenure for the justices, with 60 percent agreeing with the statement that “appointing Supreme Court justices for life is a bad thing because it gives them too much power.” One-third agreed with a contrary statement, that life tenure for justices “is a good thing because it helps keep them independent from political pressures.”
Supreme justices in Germany have limited-time appointments (12-years), so that's something that's done elsewhere.
Actually, it looks like there's a somewhat concrete (2016) proposal for 18-year mandates in the US. At least that proposal gets some attention in law reviews:
Just under three-quarters of the country think it’s time to get rid of life tenure altogether and replace it with eighteen year fixed terms. Calls to do so are coming from across the spectrum of public intellectuals. Those in favor on the left include Chemerinsky, Akhil Amar, and Henry Monaghan. On the right you find leading lights: Steve Calabresi (founder of the Federalist Society), politicians like Rick Perry and Michael Huckabee, and conservative thinkers like John McGinnis and Sai Prakash. Even Justice Breyer has said this might make sense. Calabresi, an originalist if ever there was one, argues scathingly (along with coauthor Jim Lindgren) that “Although life tenure for the Supreme Court may have made sense in the eighteenth-century world of the Framers, it is particularly inappropriate now, given the enormous power that Supreme Court Justices have come to wield.” Strong words. Moreover, the movement to limit life tenure looks positively quotidian compared to what Senator Ted Cruz has to say. This serious contender for the head of the Republican ticket in 2016 thinks you should stand for retention elections. He’s every bit as unhappy as Chemerinsky: “The Court’s brazen action undermines its very legitimacy,” he wrote, and so he wants to hold you accountable. Indeed, in tone Cruz sounds remarkably like Chemerinsky:
As a constitutional conservative, I do not make this proposal lightly. I began my career as a law clerk to Chief Justice William Rehnquist—one of our nation’s greatest chief justices—and I have spent a decade litigating before the Supreme Court. I revere that institution, and have no doubt that Rehnquist would be heartbroken at what has befallen our highest court. But, sadly the Court’s hubris and thirst for power have reached unprecedented levels. And that calls for meaningful action, lest Congress be guilty of acquiescing to this assault on the rule of law.
Effecting this kind of fundamental change would not be easy, of course, and thus is unlikely to happen. There are proposals to impose term limits by statute, the leading contender—advanced both by Calabresi and Paul Carrington—being a regular system of staggered appointments every two years and eighteen-year limits.61 But Calabresi himself acknowledges these probably run into constitutional trouble. A constitutional amendment is never an easy thing to accomplish.