Supporters of the war in Iraq as well as apologists for Mr. Bush's administration, make this statement a lot, usually, to my view, with the hope of painting critics of his foreign policy as unpatriotic, or at least dangerous. Many quite rightfully denounce the cynicism inherent in such slogan, yet they often ("always," from my anecdotal encounters with such people) miss an important point: the slogan has some validity.
If the hope of at least some of the "insurgents" in Iraq is that the US will pull out, then protests at home that aim to encourage the US to withdraw will plausibly encourage the "insurgents" to keep up their attacks on US soldiers. The participants of such protests may very well have the best concern of the soldiers at heart: what could be more supportive of them than to take them out of harm's way? Still, in the short run, these participants are, to a degree, encouraging those who would attack American soldiers.
Now, all "democratically" run societies run this risk when it comes to war. Public officials must engage in public debate and to the extent that a society is presumptively "democratic," freedom of political speech must be upheld. But those who advocate openly an expeditious withdrawal from Iraq cannot have it all ways. They should acknowledge, at least to themselves (and perhaps they do), that to some extent they are encouraging people to continue to attack American soldiers. Maybe this encouragement is minor in the grand scheme of things, and maybe such "insurgents" would attack American soldiers regardless. Still, even if these suppositions be true, that does not absolve advocates for withdrawal of all and any criticism. There are none unsullied and purely righteous, even those who fight for the right.
UPDATE 8-1-09: I changed some of the phrasing in the first paragraph for the sake of clarity.