Are the Cleary family a parody of the Clinton?

No way. They made it clear that the Cleary's were a legacy family, that have always had money, and been involved in politics for a long time. The grandma mentions her husband serving under FDR. Bill Clinton grew up poor in Arkansas, and was an unknown nationally prior to the '92 election. And Mrs. Cleary was a stay at home, drunken trophy wife. Many things can be said about Hilary, but I don't think any of those apply.

I was thinking more along the lines of a branch of the Kennedy family, probably Teddy's. This would also fit with the east coast sailing obsession of theirs. But if you wanted to make it a republican family, I could see this being the Bush family, with G.W. being in the role Christopher Walken played.