Yes, It is impossible to shut the border with either country. Nor desirable.
Since we are playing "what if..." let me put this forward.
If the US did close the borders, no more studet visas, etc.. even if as an unexpected sidee-effect trade would go down the tubes. Look at what is happening at the Amabassador Bridge crossing right now.
Unemployment would skyrocket and poverty would be rampant. It is not unconceivable that the US would break up as a coutnry in to 5 or 6 areas. The same would happen to Canada and Mexico.
Without a foreign influence to blame, the arabs would go back to fighting each other, just like they did about some centuries ago when they were close to crushing eastern Europe.
Asia - who knows. Probably lots of wars, China gets bigger then breaks up. Only Japan remains as we know it.
Latin America - nothing changes.