Actually enforcing the current laws would be a "reform", the way things are now...so we have to be careful not to stereotype the whole topic of immigration reform into meaning the worst of the Obama policies, including amnesty, etc....
It also occurs to me that you could make an analogy between federal firearms registrations and restrictions, and illegal immigrant registrations and restrictions...maybe far-fetched to some, but I agree that we can't really expect to find a practical way to deport 11 million (?) current illegals, and knowing who they are and where they live might make some voluntarily deport, and provide cause to deport others. It's all about the information...and THEY are illegal, so no concerns about that.
Close the borders to new illegals, including all these children who can be humanely "shepherded" back to their homelands, or elsewhere they might be more welcomed. Reform. Overturn the DACA rule in Congress, or reform it so it's not automatically universal. I wouldn't object to some illegals being allowed to stay, for purely practical reasons (CAN we realistically deport 11 million people?!) BUT their status would have to remain illegal, even if not subject to deportation, this could not apply to ALL illegals, and any privileges of citizenship beyond not being deported would have to be earned the same way as legal immigrants do...get in line. That would be a reform.
What's "broken" about our immigration system right now is just that the laws are not being enforced, we're allowing the borders to be seriously breached by illegals, and the lottery system and "rules" regulating how many persons can legally apply to immigrate from any given other country are cockamamie and arcane.
So, I'm in favor of THAT "immigration reform", LOL! Each part in it's proper order, should take care of the problem. Of course, no one in their right mind would be in favor of "comprehensive immigration reform" that we would "have to pass so we know what's in it...don't mix that up with real and needed reforms and changes, though!