The troop surge was part of the final victory but not all of it. It took a long time to win over the average Iraqi because they didn’t trust the U.S. - and for good reason.
1) Bush the Elder did not finish the job after the first Gulf War. He did not remove Hussein from power. Bush told Iraqis to rise up and overthrow their government. Many did, and hundreds of thousands were mowed down by Hussein while all we did was enforce a “no fly zone”. I will never forgive Bush for that. Why would we would we expect the Iraqis?
2) After the second Gulf War there were a multitude of Democrat traitors saying the war was a mistake, “Bush lied-people died”, we would pull out the troops, etc. Would you throw in with the U.S. in that environment? I wouldn’t. I would lay low until it was clear who was going to be the winner, which side had staying power. That’s exactly what the Iraqis did. Bush’s re-election, followed by the troop surge, showed the Iraqis the U.S. would stay on for victory. This is what won over the Iraqis and won the war. A troop surge early on may well have failed because we had not yet garnered the trust of the Iraqi people.
And who was the lead politician in the US pushing for the surge to demonstrate US resolve to stay the course?
McCain.
I loathe him for campaign finance, amnesty and general back-stabbing. But I also will recognize that he exercised courage to push for the surge when doing such was widely viewed as political suicide.