We are not in Iraq to fight Al-Qaeda, despite what those digging for justifications say. We are there to stabilise a government and civil society that we destroyed through our own ineptitude in the invasion. Al-Qaeda operatives are in a lot of countries, and there are also "homegrown" terrorists that aren't even linked to Al-Qaeda in a lot of countries (e.g. the U.S.). Killing them in Iraq, or having them run to other countries (e.g. Afghanistan) will not solve the problem. There are always more, too.
What the Republicans have done is tried to invade a country on the cheap and under false pretenses. This failed miserably, and it's now become a hugely expensive operation with no clear end in sight. So Al-Qaeda was pulled out of the hat as the bogeyman and, yes, about a thousand Al-Qaeda fighters are in Iraq out of several million other people who don't like us either. They are there largely because of the complete vacuum of authority, which is due to the horrific bungling of the occupation.
So now the Republicans dig deep and come up with "the troops" as the justification for the occupation. We see staged question-and-answer sessions in which soldiers ask commanders questions right out the Republican talking points. The upshot is that, even though it's hugely expensive and doesn't advance our foreign policy objectives, we have to keep supporting the occupation forever or else the troops will lose the will to fight.
It's not about "winning" or "surrendering". There is no one to "surrender" to. The Iraqi government is incompetent, so there is no "winning". It's about bullying them into giving up their oil with the Hydrocarbon Law so that we can focus on keeping the oil fields secure and letting the rest of the country go to hell. A few oil companies get rich, the consumer pays high gas prices, and the taxpayers foot the bill and get to pay for the refineries and infrastructure, too. That's how we "win".
