My recent experience in this may not matter much, depending on how similar the Jetta and Golf lock mechanisms are. (The Golf mechanism is akin to trying to push a door open by pushing against 3 people standing loosely shoulder to shoulder, with the middle one normally turned slightly askew but temporarily straightened by the electrical actuator. If he doesn't quite turn straight, your shove doesn't reach the door.)
Look at pictures first, and if it's not similar, never mind this.
I've never had anything break on my Golf, but it jammed up for the second time recently.
At first, it would sometimes refuse to open, but after another drive or so (or just waiting for the actuator to reset, and trying again) it often would.
Eventually it stopped workign altogether, and even more eventually, I started to look into it.
I climbed into the trunk, and sprayed some cheap electrical contact cleaner (the least messy creeping cleaner or lubricant I have) with the little red tube between trunk molding and lid molding, trying to aim it upward towards the inner lock mechanism.
I forget if any of it got up in there or if it was merely the cleaning of the latch that let the marginal mechanism move a little easier, but it opned immediately, and it was very obvious that gummed-up or lacking lubrication in the parts moved by the actuator and nearby were the problem.
I cleaned and lubricated both that and the latch, and identified the point of the linkage nearest the latch that will open the trunk for sure, if one just pushes it hard enough.
Then I measured out the location of that spot on the trunk lid trim panel, and drilled a finger-sized hole into the panel. Next time it sticks, all I have to do (if the single working folding seat release doesn't pack in by then) is climb in and stick my finger through the hole and push sideways.
I've been meaning to post the precise measurement for that hole (a few inches from the bottom, and slightly to the driver's side), since even when it's too late and the lid is utterly stuck, this surgery from inside the trunk is easy (easier with a Forstner or other large drill bit, but OK with a smaller bit and a knife) and works regardless of specific defect.
Something similar might work on the Jetta.