Not something I've done many times, but when I have I used router to cut through, not a jigsaw.
It depends what modification you are trying to make, of course.
If you are forced to work in situ, have you considered that neither machine will get close to a rear wall on other vertical surface above the worktop.
With a narrow slot router blade, you can control the cut to avoid anything below the worktop. If the exposed edge of the laminate is important to be non-jagged afterwards, a router, nibbled away in small stages, does a better job.