We are more apt to win it with the Dems, in fact, in charge. They will be totally in charge after 08 and will pull back from everywhere and and beef up Homeland Security and turn its focus entirely toward Christians and Conservatives and gunowners. The mohos will successfully hit us with a 9-11XXXX, perhaps a nuke and the administration will sic the FBI on them to scrape up the atoms of the suicides and Bring Them To Justice. Then it will happen again. And again. Each will be bigger and finally the Democrat-In-Charge will understand that the mohos are not really his allies in the war against rich nonDemocrats and will be exasperated and enraged at the "stab-in-the-back" from the Democrats' erstwhile proteges. In his panic he(or she, as it were) will launch against Islam and take over the American economy, what's left of it after the moho strikes, and dissolve the Constitution. America will win it in the end but the destruction will be immense, materially and to America as America.
With the Republicans in charge we are faced with endless pussyfooting as they tailor every action to show the Democrats that Republicans really are nice, compassionate even. That too will lead to strikes on the homeland- but will keep them away longer- and measured responses that do not convince the saracens that Allah does not will them to prevail. Ultimately the Democrat scenario is probably the one more likely to ensure that the West survives without a Caliphate but it won't be much better.
I don't really think that the Dems believe the Islamofascists are their allies. They were just willing to use them to get what they wanted, i.e. power. Now that they've got it, though, maybe they will stop trying to undermine our government's efforts in this war. I think that the Dem leadership might at least stop doing that, although I believe that there are a lot of rank-and-file Dems who can't turn on a dime so easily, and are not smart enough to understand that the Dems have pursued this strategy of undermining our government purely for their own political gain, and not for any principled reason.
Your assessment is harsh and depressing. However, they way things look today, it seems possible that it will play out just as you describe. Watching the coverage of this Iraq study group today has me ready for a straight jacket. It looks like the entire country has gone senile.