First would be to remove most Democratic power in the Congress, allowing re-election paranoia to cut way back on govt spending and pork programs...then put what ever is needed into the security program...by using military and Border Patrol input as the basis...to make it tedious and unprofitable to cross over in large numbers for the cartels; then clamp down harder on business and individuals per existing laws and regulations to make it inhospitable for illegals to openly work with stolen ID and fake documentation. This would use many employed Fed workers and at least get some use out of the underused Federal, State, and local gov't workers whose Unions have created a paradise for incompetent employees.
Remove at almost no cost unqualified Welfare recipients from the rolls and see that Americans get the actual help the program was designed for.
No proof of citizenship, with criminal penalties for false ID, will dry up the flow by more word of mouth than actual feet on the street...also cheaper than hiring new workers in the overpaid and overfull Gov't.
Once this has become the norm and the Border has become a harder nut to crack, the fewer avenues available to smugglers and others will be much easier to monitor.
There will always be a way through a controlled situation whether it's a border or a regulated environment; the gov't needs some covert access, LE needs some flexibility, and just societal pressure needs some small relief.
So..."perfection" aka Korea or the Berlin Wall? Not that much needed...just close enough. Reduce the flood to a trickle, and maintaining it will be easier and cheaper.
Let the pendulum swing hard back the other way for a few generations.
We need millions more of Thai, Somali, Greek, Korean, Chinese, Laotian, Kenyan, and Russian immigrants instead of
many millions of Mexico's lowest level of citizens.
I love many individual Mexicans, but I can't handle the tsunami of crap Mexico has sent us.
Maybe later I'll tell you how I
really feel...!

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