I've always found this "War on ______" phenomenon to be something really weird about American politics. In the rest of the civilised world, a government will generally "increase anti-drug policing measures", or "expand targeted health-care spending" or "make affordable housing a higher priority", instead of declaring wars against drugs, or AIDS, or poverty. It just strikes me as a really strange way to think about social problems.
The "war on terror" is a different kettle of fish entirely, though, because it involves actual warlike combat operations, and infringements on civil liberties, with the implication that these are temporary measures with defined goals. It's well and dandy to fight a definitionally unwinnable war against poverty in order to improve people's lives. The analogue of this would be to fight terrorism where possible, up to the point where fighting terror becomes too detrimental to other goods. The analogue is definitely not fighting The War On Terror in the particular form it currently takes, and it's a fallacy to say, just like we can never eliminate poverty but have to keep trying, we have to keep doing what Bush tells us is necessary to fight terror, and do it into the indefinite future. It's an important distinction to make.