The Republicans should just pass whatever immigration bill they can get through the Senate, and tell Obama to either sign it or veto it. If he vetoes it, they can say he preferred his own executive actions to Congressional legislation on the exact same topic, which wouldn't give him much of a leg to stand on. He pretty much has to sign whatever immigration bill Congress sends him now.
The thing is, McConnell and Boehner have said that if Obama goes through with this executive action, they'll refuse to negotiate with the Democrats about immigration reform.
Oh, how unfortunate that they found an excuse not to negotiate.