I've argued before, on this blog and elsewhere (see below), that the Senate should abandon the filibuster. Whether or not the Supreme Court would actually strike it down, though, is difficult to say.
Filibuster supporters could point to the fact that the Constitution gives the Senate the authority to make it's own rules. Also, while it is true that the Founders intended majority rule in most cases, they could argue that the 60 vote requirement for cloture is not the vote on the bill -- it's the vote to end debate on the bill. The outcome of such a case would depend, in part, on whether the Supreme Court finds that to be a distinction with, or without, a difference.
For more info on the filibuster, see:
Why Don't U.S. Senators Filibuster Anymore?, Suite101