Actually, they shouldn't: Groucho's funny because he's lampooning "whatever it is, I'm against it," and the Republicans in Congress and elsewhere aren't funny (ridiculous, perhaps, but not funny) because they're quite serious about it.
(Video here, since I can't seem to figure out how to embed in Typepad.)
I don’t know what they have to say,
It makes no difference anyway --
Whatever it is, I’m against it!
No matter what it is or who commenced it,
I’m against it.
Your proposition may be good
But let’s have one thing understood --
Whatever it is, I’m against it!
And even when you’ve changed it or condensed it,
I’m against it.
Conservatives these days come pre-parodied.