What does “raising the debt ceiling is not groovy” mean? Is the word “groovy" obsolete among the youth of America”?

Groovy can also simply mean "good." It's a lot like "cool:" it can mean almost anything, almost always in a positive way. So translate it as "raising the debt ceiling is not good".

I personally use "groovy" occasionally (I'm 30, so not "youth" by most measures), but I'm aware that it's a bit of an eccentricity on my part. I picked it up from a 40-ish California hippie several years ago, and I don't think I've ever heard it used by anyone younger than that, so it's probably virtually obsolete in gen Y. < /anecdotal-evidence>

Groovy is very much a dated word in the US; the word is seen as a throwback to the 60's or 70's. What the ad actually says is that Santorum voted for the biggest entitlement increase "since the 60's---not groovy". The word is being used in the ad to complement the reference to the 60's.

I'm not sure exactly what's being asked here, but:

Groovy as a slang term meaning "fashionable, attractive and interesting" is what you would called "dated slang". People are aware of its existence and meaning, but it's out-of-date. Therefore, intentionally using dated slang would tend to be a way to say that someone is "out of touch".

Both "groovy" and "dude" are slang terms which achieved wide popularity from the late 60s to early 70s as part of the hippie culture. And like hippie culture itself to a degree, the term "dude" came back into fashion in the '90s and still maintains currency. I don't think "groovy" ever made such a comeback, though.

So I think nohat's answer, that "groovy" is deliberately chosen as a dated expression, correctly explains the ad's choice of the word.

In addition, though, the informal usage "not [slang word for good]" is itself a way to say "emphatically not good/not acceptable", without necessarily retaining the particular sense of "goodness" in the word. For example:

"Hey dude, talking to a girl like that is not cool."

This does not mean merely that you are not good-looking and fashionable (which is what cool means), it means you are rude, inconsiderate, and many other forms of bad, going far beyond lacking coolness.

There's also the expression "not kosher", meaning "not allowed" or "against the rules", and it can be applied to things that have nothing to do with Jewish dietary rules.

So "not groovy" does not just mean lacking fashionability or trendiness, it means just plain bad, and can apply even to economic policy.