Whoever doubted that Ameican soldiers could prevail over rag-tag insurgents?

Answer: Obama. And more than once:

Actually, however, Obama opposed the surge not because of those "factors" but because he thought it would fail. He said, on January 10, 2007, on MSNBC:

I am not persuaded that 20,000 additional troops in Iraq is going to solve the sectarian violence there. In fact, I think it will do the reverse.
On January 14, 2007, on Face the Nation, he said:

We cannot impose a military solution on what has effectively become a civil war. And until we acknowledge that reality -- we can send 15,000 more troops, 20,000 more troops, 30,000 more troops, I don't know any expert on the region or any military officer that I've spoken to privately that believes that that is going to make a substantial difference on the situation on the ground.
On March 19, 2007, on the Larry King show, he said:

[E]ven those who are supporting -- but here's the thing, Larry -- even those who support the escalation have acknowledged that 20,000, 30,000, even 40,000 more troops placed temporarily in places like Baghdad are not going to make a long-term difference.
On May 25, 2007, in a speech to the Coalition Of Black Trade Unionists Convention, Obama said:

And what I know is that what our troops deserve is not just rhetoric, they deserve a new plan. Governor Romney and Senator McCain clearly believe that the course that we're on in Iraq is working, I do not.
On July 18, 2007, on the Today show, he said:

My assessment is that the surge has not worked and we will not see a different report eight weeks from now.
On November 11, 2007, two months after General David Petraeus told Congress that the surge was working, Obama doubled down, saying that the administration's new strategy was making the situation in Iraq worse:

Finally, in 2006-2007, we started to see that, even after an election, George Bush continued to want to pursue a course that didn't withdraw troops from Iraq but actually doubled them and initiated a surge and at that stage I said very clearly, not only have we not seen improvements, but we're actually worsening, potentially, a situation there.

http://www.powerlineblog.com/archives2/2008/07/020997.php

There are two parts to it:

(1) He was talking about the surge by itself. In the same speech that those excerpts come from, he specifically mentioned that you'd have to see help from the Sunnis and Shiites, as well. We did see that, so it helped.

(2) He was talking about the political solution, not just a temporary cessation in violence. I thought the point of the surge was to allow the Iraqi government room to meet the "benchmarks". Has that been successful by your reckoning?