Is “Better never than late” the saying as popular as “Better late than never”?

You won't find this definition anywhere, because Maureen Dowd made it up. It's a play on words, a reversal of the familiar trope that is meant to be funny or to make you think. In this case it would seem to be rather sardonic, intended to mock the Republicans' new-found "compassion."

That said, I'm a bit puzzled myself because turning that particular trope around isn't exactly a deft attempt at humor. I think she means that it would be better not to have faked compassion at all than to come on it in this way at this time. But it is an awkward effort. I don't know Maureen Dowd's other writing, but after reading the entire article I believe she may be concerned more with slamming her target as hard as she can than with making people laugh.

Oh, well — not everyone can be Jon Stewart.

Further Reading

The inversion of a trope exhibited here is a familiar pattern known as a transpositional pun. Check the link for some other examples. Here's what the Wikipedia article says about their effectiveness:

[T]ranspositional puns are considered among the most difficult to create, and commonly the most challenging to comprehend, particularly for non-native speakers of the language in which they're given (most commonly English).

No wonder Oishi-san had trouble with this one. I myself am still having trouble with it. Unless all parts make complete sense when reversed, the inversion fails. For contrast, here's one (from the linked article) that does work:

Hangovers: the wrath of grapes. [Inversion of "the grapes of wrath," a line from Julia Ward Howe's "The Battle Hymn of the Republic" that Steinbeck used as the title of what was arguably his greatest novel.]

"Better never than late" apparently occurs 1730 times in Google Books, so it's not exactly a "coinage" by Dowd.

It's a fairly "easy-to-think-of" variation on the well-established maxim "better late than never" (that's 140,000 instances), and it only takes a little more thought to see what it must mean. Here's a pithy summary...

Some people are too late for everything but ruin; when a nobleman apologized to George III. for being late, and said, "better late than never," the king replied, "No, I say, better never than late."

"Better late than never" is not half so good a maxim as "Better never late".

In short, you'd only use it when you want to emphasise how bad "late" is - either because you're bitterly attacking someone for already being late, or you're warning them not to be late, because timeliness is of the utmost importance in the current context.

It isn't really an expression. Rather, as FumbleFingers says, it's an easy-to-think-of variation. Some other examples include:

• Better sorry than safe
• Make ends overlap
• Life before death (used by Christian Aid)
• Quantity not quality (used by one of my college classmates in relation to the volume of coursework we had to do)
• Cross this bridge when we're nearer to it

Most such sequences of words have probably been thought up and used by many people independently of each other.

A good use of "better never than late" is for situations in which something is no good if it's late, such that if you end up being late with it then it was a complete waste of time (and possibly money etc.) to undertake it in the first place. When I was at university and the time came to undertake our final-year projects, we were warned that if we are late handing our work in then it will score zero, which is ridiculous as it means exactly this.

"Better never than late" is an expression I heard on the radio by a man in the military. It means: React quickly to a threat. If you take too much time looking for the ideal cover, you'll be dead. Trust your training to make the correct decision. It's a twist on the opposite phrase to make it memorable to the broad population. Of course it's also applicable to some everyday situations.