So how do we defeat the jihad against us? Define "we." And keep killing jihadis.
Sure, decapitating jihadi terrorist organizations by killing or capturing their leaders doesn't destroy them given the fanaticism that motivates the jihadis to kill. But it does help disrupt them.
And it is rather necessary.
It doesn't matter that the public is tired of fighting jihadis. If we stop fighting them over there, the jihadis just figure they have a clean shot at us over here.
And don't you dare say that our wars against jihadis is what inspires them to kill us at home.
But jihadis can be demoralized. The Iraqis demonstrated in the Iran-Iraq War that if you keep killing jihadis in large numbers and keep defeating them, they can break. We clearly aren't killing enough jihadis.
Remember too that ultimately that killing our enemies is just a necessary holding action until the Islamic world--where we do have a lot of allies fighting on our side, don't forget--wins their civil war over who gets to define Islam: the jihadis or normal people willing to tolerate non-Islamist Moslems or non-Moslems (That is, not kill them or oppress them when living among them. We don't need them to love those who are different.).
When that civil war is won by the good guys, the recruiting pool for the jihad will dry up to a manageable trickle that police forces and intelligence agencies can deal with.
Remember too that if your premise is that we can only do what the American people will support, if we are hit hard enough at home with even bigger and more horrific terrorist attacks than 9/11 was, the American people will support a whole lot of killing. Do Hiroshima and Nagasaki ring a bell? Let's not go there.
Don't make the long war longer by thinking we can decide it is over before our jihadi enemies do.