See, I think this is an area that both liberals and conservatives can agree. If you want to end illegal immigration, take away the job opportunities.
Personally, I'd prefer a more graduated system. For example, you might hire a nanny and not even think to check for legal status. Should you have to eat a $40k fine? Probably not. But you should have to eat, say, a $500 fine the first time.
Any employer repeatedly caught should see drastically increasing fines. Maybe on the third strike you go to $40k. The net effect would be the same (illegal immigrants would leave) but it'd be less draconian.
The second step is that we'd need to re-think our legal immigration process. We're too reliant on cheep labor to just cut off the pipeline of new immigrants entirely. Right now it's completely un-sellable to suggest opening up the spigot of legal immigrants. But if we were able to get illegal immigration under control, I think a lot of people could come to a consensus on opening up our borders more to legal immigrants.