I've always been curious if the "problem" from the popular-support perspective was the casualties (which, while high, were not THAT high for the total force -- in Iraq, most were due to IEDs/rockets and spread over a large number; in Afghanistan they're a bit more concentrated on actual combat troops), or the lack of progress, or some combination.
There really was ~zero progress (net; there were some wins and some losses) from late-2003 to early-2007 in Iraq, overall, and from ~2003 to ~2009 in Afghanistan (the 2009 end date is questionable; I'm reluctant to say Afghanistan overall is better right now than it was right after the CIA/ODA 555 operations in late 2001, as described in First In by Gary Schroen).
I was in Iraq watching this and was a lot more critical of the way the US was fighting from 2003-2006 than of the actual casualty numbers.
It's certainly more rational to be more willing to take a few hundred casualties if it brings a quick victory than to endure long slow bleeding of thousands, but I don't know if popular opinion is rational. I think casualties-per-second are much higher in offensive operations than in purely static defense, though.
There really was ~zero progress (net; there were some wins and some losses) from late-2003 to early-2007 in Iraq, overall, and from ~2003 to ~2009 in Afghanistan (the 2009 end date is questionable; I'm reluctant to say Afghanistan overall is better right now than it was right after the CIA/ODA 555 operations in late 2001, as described in First In by Gary Schroen).
I was in Iraq watching this and was a lot more critical of the way the US was fighting from 2003-2006 than of the actual casualty numbers.
It's certainly more rational to be more willing to take a few hundred casualties if it brings a quick victory than to endure long slow bleeding of thousands, but I don't know if popular opinion is rational. I think casualties-per-second are much higher in offensive operations than in purely static defense, though.