Bill Scher does a nice job in the Washington Monthly of laying out the history of immigration reform efforts. Very instructive, though I'm not so sure about his solutions to the current dilemma. And while you're at it, this article from the Post lays out the pickle the Biden administration is currently in. As the article notes:
"The situation at the border — which Biden and his advisers steadfastly refuse to call a crisis — is the result of an administration that was forewarned of the coming surge, yet still ill-prepared and lacking the capacity to deal with it. Administration officials have been plagued by muddled messaging, sometimes making appeals that seem directed more at liberal activists than the migrants they need to dissuade from coming to the country."
Yep, they've put their finger on it.