The solution is not to let everybody in who wants to make a buck. There are zillions of folks who want to come here and we only have so much room. Nor is the solution to reward lawlessness by providing a path to citizenship because that only encourages the bad behavior. The solution, which will never be embraced, is to ban any and all future amnesties which reward this behavior with jobs and opportunities and citizenship.
You relax visa numbers on the seasonal jobs (H2 visas), educate as to the legal way to pursue these jobs and existing green cards through the governments of these countries, crack down big time at the border, and start sending a bill (which, granted, will never be paid) to the countries in question for the cost of returning their citizens. You allow them a way to register and utilize these increased visas without penalty. That is, they aren't subject to the usual multi-year bans for illegal entry and/or presence for those specific visas and those visas only (let's call them special visas). The trick is (1) they don't get some special path to citizenship, and (2) they are still subject to the multi-year bans when they pursue regular work visas. This isn't that big of a deal because the wait time on the visas they would be pursuing (unskilled labor) is currently 3 1/2 years and will increase as the demand goes up for them. But if they fuck up again, the clock starts fresh on their multi-year ban again, and they become ineligible for future special visas. I've outlined something like this plan several times on the boards over the years. I think it could actually work because you aren't getting people a place at the front of the line and they are still subject to having to wait 3 or 10 years (usually 10 for the types we're talking about) before they can even get a green card, and that green card is gained within the way the current system is set up and not by some special amnesty visa like it was with Reagan's amnesty. It is also different from Clinton's amnesty because his formally waived the 3/10 year bars, which meant all you needed was a job offer and $1000 and you were good to go.
I will say, however, that the longer the current debacle goes on, the more receptive I'm going to be for a plan to dig a fucking moat at the border, stock it with alligators, and add about 200 yards of minefields after that.
We also need to overhaul our family-based visas. Wives and unmarried children should be able to piggyback as they do now. Any other family should not be able to petition for a green card visa based on their relationship with a citizen or permanent resident. That would include siblings, married children, unmarried adult children (over 21) and parents. Some of those have to wait about 20+ years anyway, so getting rid of that isn't a big deal. Parents are a bigger deal, particularly with Asians who take care of their parents when they are elderly, but so be it. This allows the family-based system, which usually involves the most unskilled, to be narrowed and targeted.
Congress also needs to pass legislation to specifically outlaw actions such as DACA without Congressional consent. Cruz's proposal is too broad and just bans everything. He needs to specifically target things like TPS and other loopholes that the President feels he can exploit without Congress's go-ahead.