Most people think they already did, at least in Iraq
It has become obvious to the average Iraqis, who are now the victim of attacks far more than coalition forces are (check that table again), that the objective of the insurgency is not removing the coalition (the "Freedom Fighter Theory"), but destroying Iraq's chances at becoming a free society (the "Baathist/Islamist Thug Theory").
Almost all the captured insurgents in recent months have been turned in by Iraqis.