I was just at a panel at DunDraCon hosted by Kenneth Hite, and his assertion about this very subject was that, ultimately, Lovecraftian horror isn't about whether or not the players can kill things. It's that doing so is hopeless and futile. The threat of Cthulhu and such isn't merely personal oblivion, it is apocalypse, the complete breakdown of the natural order in the face of overwhelming and uncaring cosmic apathy and spite. GMs are encouraged to break the laws of physics, attack family and friends, and bring about eerie coincidences with disturbing implications for the nature of reality. All combined with the maddening realization that, even together, they are truly alone in the world for knowing about the threat at all and being unable or unwilling to doom anyone else with that knowledge: not friends, not authorities. The Mythos is almost like a virus which the protagonists think they can fight by isolating themselves from the rest of society and/or trying to attack the darkness.
The Dresden Files, though, is more about the players getting kicked around a lot before pulling themselves up by their bootstraps and saving the day. There are a significant number of factions which know about the nature of threat of the Outsiders, and they are empowered (or at least informed enough) to respond to it (some actively oppose it, others have accepted their power). And true: every Dresden story has an ever-growing thread of eventual doom, centered on an eventual Outsider incursion. It isn't *necessarily* the right venue for Lovecraftian horror, but it can be made to be.
Go back to the basics: the threat to family and friends, the danger of involving outside help, the isolation. Remove allies. Harm loved ones. In implausible and insane ways. Implicate the heroes in the very Mythos threat they are trying to fight, so now the very people they might trust for help - the police, the White Council and/or the Venators - are out to get them, and put them down hard. Make sure that the only out is through, and that "through" means giving up what is important to them.
And your players will need to *want* to play a horror game. It's not something you can really spring on them. The most common thing I hear is that the players need to be receptive to it because they just can't be forced to take it seriously otherwise. Anything can break that spell.
