Right, and you now have variables under your control to drive their power requirements arbitrarily high -- namely, the better your timing, the higher your effective S/N ratio (because your spread-spectrum signal can be, in effect, very-very narrowband, but hopping all over).
You increase your timing accuracy by 10x, and the jammer's power requirements increase by 10x (crudely speaking -- not a 1:1 trade, but directly linked).
That's a different kind of spread-spectrum. That's a frequency-hopper, where the carrier changes frequency (the first SS- an idea attributed to Hedy Lemarr in the lore).
We're talking about direct sequence, which increases the bandwidth of the signal but keeps the same carrier. To jam that (theoretically) you need large power through the entire band.
I was talking about both -- for the purposes of explanation, frequency-hopping is more intuitive. (I was trying to be responsive to @Redfern above, who mentions frequency-domain jamming.)
Both frequency-hopping and direct-sequence spread energy over a larger bandwidth. Direct-sequence does not explicitly frequency-hop, but the time-domain switching it uses will spread the energy out in Fourier space.