Escalation would imply a broad increase in the scale of fighting, with both a significant change in the scale of forces, and a more aggressive or biligerent set of tactics. Launching an invasion of Syria, for example, would constitute escalation.
Launching an invasion of Syria would be opening a new front, not to mention insane. A huge increase in numbers is not possible, but the change in tactics is really all that's needed.
Putting 15,000 more boots on the ground in Baghdad will ratchet up the level of violence, in a way that's likely to stick even if the solders are drawn back. More of our peeps are targets, more get killed, looser rules of engagement to kill back... even though troop numbers are not permanent (they can't be), the intensity of conflict/pace of death will be bumped up for a lot longer.
It would not be surprising to see the inevitable numerical drawback replaced by increased airforce action. It's escalating. Going from 50,000 to 650,000 in vietnam wasn't one move. It's incremental. As I said we don't have the manpower for that kind of numeric escalation, but we sure do have the technology to start killing more people (which is what the backers of this are really after when you read it).
If you look, the strategic thrust here is to put more combat troops in trouble spots and try to rein in the Shia militias, who we have not really fought against. This would most likely bring a couple million more trigger-fingers (or IED detonators) to bear on our supply lines, prompting some additional reaction in defense.
Since the whole deployment is hopelessly vulnerable from the supply-chain standpoint (no number of HUMVEE escorts will make it secure), the likely response will be large and blunt, designed to deter rather than actually prevent, increasing guerrilla attacks; likely much in the style of Israel vs Palestine.
Once we start blowing up populated apartment blocks with A-C130-fired howitzer shells to wipe out suspected safehouses, it's all downhill from there.
