The "apologize, pay a token fine, get a work permit" crowd thinks violating immigration laws are like speeding, pot, or jaywalking laws. The "deport them all" crowd thinks violating immigration laws is like stealing or committing fraud.
That's why this issue won't be resolved any time soon. If liberals get a big enough majority there may be a one time amnesty or a change that allows new immigrants in. If the right got a big enough majority there would be a one time mass deportation or maybe a stupid wall. But the bottom line is that some people see it as no big deal, the others see it as a heinous crime, and it's a Rorschach test: agreement on who's right will never happen.