Does the West / USA / NATO have the strategic patience to campaign against the 'Accidental Guerilla' and those who are closer to the global jihad / AQ?

I am mindful of the overwhelming majority in many NATO countries that are opposed to the deployment of military forces; in the the UK cited at over 80%. How can we engage in COIN when there is little public support.

(At times this theme has appeared in various threads, IIRC not recently; perhaps itself a sign of attrition).