I understand the interest of business lobbies in getting cheap, unskilled labor through amnesty.
It appears to be me that the reason the ruling elites insist on "comprehensive" immigration reform (i.e. strong border enforcement, mandatory employment status checks, blanket amnesty, etc.) is precisely to cause political gridlock and thereby maintain relatively open borders, employer deniability, limited legalization, etc. There are now whole business sectors that require an unlimited pool of illegal (and therefore easily exploitable) workers. Thus neither political party is interested in putting a stop to the current situation regardless of what the ordinary taxpayers want.
Otherwise, there's really no pressing need to make illegals into citizens. We could continue exploiting their labor - they're pretty willing to work without citizenship.
Once all these illegal workers become legal, will they be fired and a whole new crop of illegals have to come in to replace them?