It tells us that he isn't much of one, and that his first instinct is always to make the problem go away, not to solve it.
From Andrew Sullivan:
Some actual reporting from yours truly. It seems clear from sources close to Grenell and reporters on the foreign policy beat that his turning point came last week. He'd been part of organizing a conference call to respond to Vice President Biden's foreign policy speech, now known best for the "big stick" remark. So some reporters were puzzled as to why Grenell, a week into his job as Romney's national security spokesman, was not introduced by name as part of the Romney team at the beginning of the call, and his voice completely absent from the conversation. Some even called and questioned him afterwards as to why he was absent. He wasn't absent. He was simply muzzled. For a job where you are supposed to maintain good relations with reporters, being silenced on a key conference call on your area of expertise is pretty damaging. Especially when you helped set it up.
Sources close to Grenell say that he was specifically told by those high up in the Romney campaign to stay silent on the call, even while he was on it. And this was not the only time he had been instructed to shut up. Their response to the far right fooferaw was simply to go silent, to keep Grenell off-stage and mute, and to wait till the storm passed. But the storm was not likely to pass if no one in the Romney camp was prepared to back Grenell up. Hence his dilemma. The obvious solution was simply to get Grenell out there doling out the neocon red meat - which would have immediately changed the subject and helped dispel base skepticism. Instead the terrified Romneyites shut him up without any actual plan for when he might subsequently be able to do his job. To my mind, it's a mark of his integrity that he decided to quit rather than be put in this absurd situation. And it's a mark of Romney's fundamental weakness within his own party that he could not back his spokesman against the Bryan Fischers and Matthew Francks.