This post from The Corner seems like a good, commonsensical idea to me.

If an illegal immigrant is injured while working on private property, instead of absorbing the costs of his treatment (which they cannot reclaim from state Workmen's Comp schemes since the worker is not covered), hospitals and municipalities should sue the property owner to recover those costs. A few well-publicized prosecutions like this -- even unsuccessful ones, which could still cost the defendant a bundle of money in legal fees -- would have homeowners clamoring for guarantees from home-service contractors that their workforce does not include illegal entrants.