Let me assure you people making that claim are trying to spin their way out of being out of step with Reagan on the immigration issue or are just in total denial. I lived here in the 80s and let me assure you enforcement was not much better than now. And further, the flood of illegals became a title wave after the 1986 amnesty. Those who claim despite the amnesty that there was greater enforcement are arguing against the historical reality that while the bill provided for greater enforcement, none was forthcoming in the subsequent implementation of the legislation.
Many of these same conservative opposing the Senate bill now are even saying "We were promised enforcement in '86 and weren't given any" as part of their rallying cry against current guest worker plans. They are being mightely inconsistent, and not just a bit dishonest, now flip flopping and saying there was in fact enforcement. It's not true and it's all to cover their rears on the Reagan front.
Whether you know it or not you're making the point for us. Illegal immigration increased after 1986 precisely because the amnesty failed. It makes no sense to do it again as Chris Cannon wants to. Even Ed Meese, Bill Bennett and others of that era are saying so, not until at least the borders are secured, then maybe they can talk about it.