Basically nobody opposes deporting actual criminals

Deportation as a mechanism of punishment for state and federal crimes is generally bad policy. It is excessively draconian (it effectively renders them homeless, unemployed, and indefinitely denied their family and friends for... what? Too many parking tickets? Working construction without a license? Illegally camping?) for some. And entirely too lenient (deporting hardened criminals and cartel leaders like serial rapists or murderers effectively guarantees their release in states that can't afford to jail them) for others.

That's why we'll often extradite gang leaders into the US from overseas, when the crimes are severe enough. Its also why "sanctuary cities" regularly look the other way for petty offenses in order to avoid the mass economic disruption of ICE interference in municipal matters.

Injecting immigration penalties into the civil justice system fucks with all the basic functions of local courts and prosecutors. It raises the stakes on minor offenses and gives the worst offenders a get-out-of-jail-free card.

All that is assuming you even have somewhere to send undocumented criminals. For people who are functionally stateless - migrants who came over as children without papers, refugees from countries that cannot repatriate them or effectively no longer exist, Native Americans who the Feds don't want to recognize as legal US residents - the ability to deport is little more than Penal Transportation. Nevermind how it routinely violates the 5th and 8th amendment, it mostly just means bribing a small, bankrupt satrap of the US to accept planeloads of random people, often without so much as a proper conviction.