For those of you who aren't familiar with the idiom, it actually goes back all the way to the 1801 play The Knapsack by English novelist Maria Edgeworth:
In this sense it was a description of the way the marching soldiers literally held their heads up which, for anyone familiar with doing any sort of long distance walking, was a sign of alertness and confidence.
They marched, and I amongst them, to face the enemy -- heads up -- step firm -- thus it was -- quick time -- march!
By the beginning of the twentieth century heads up began to be used as an adjective, probably based on the sense of alertness and confidence that comes from holding your head up while performing any activity. An example of this is:
Somewhere around the late 1970s or early 1980s a noun form arose which could be used as an advance warning of something. An example of using heads up as a noun is:
McGee was right on the job, and looking heads up.
This noun form probably came from a shortening of phrases like "heads-up alert", used by The Washington Post in 1979 to describe a warning by intelligence officials about unauthorized diplomatic contacts. Regardless of the origin, heads up is now very commonly used as an advance warning of something.
McGee's heads up came just in time for Tony to avoid the stapler that Ziva had thrown at him.
So should heads up have an apostrophe? If you think about the words, what is literally being communicated is that all involved in a situation should have their heads up, i.e., be aware. Given that usage there is no need for an apostrophe implying either possession, or one for the elimination of a word like 'is' or 'has'. However, that doesn't mean that you can't use it that way. For example:
That one particular example aside though, no apostrophe is needed, and no dictionaries include definitions with one. You'll have noticed from my examples, though, that I've used both "heads up" and "heads-up". Mirriam Webster includes both as valid spellings, though most other sources seem to use just the "heads-up" spelling. Both work, though using the hyphen may be advisable since more definitions do use it that way.
"Heads-up, McGee," Tony yelled over the radio. "He's coming your way."
"My head's up, Tony," McGee shot back. "I've got it covered".
One last note. It is possible to use heads up with a completely different meaning. For example:
This meaning is that of someone being in charge of a particular function, so don't confuse it with trying to warn something about something -- another reason to use the hyphenated version as I mentioned above.
"Deputy Director Craig heads up the covert division, McGee," Tony said quietly, hoping that he wouldn't be overheard.
Mirriam Webster Online
Online Etymological Dictionary
Word Reference Forums