They were the ones to lobby the residency bottleneck into place for that purpose, yes, but recently the problem has become so acute that they have been (at least pretending to) push to expand the cap. Their bet on systemic dysfunction payed off a bit too well and they are keenly aware that if they are seen as part of the problem they will have less say in the solution, so at the moment they are allies.

As of a few year ago, anyway. I haven't been paying attention recently and the situation may have developed.