If you want Mexico's help on the border, find a way to tax Mexico for violations of the border. Miller acknowledges the challenges to implementation. It necessarily includes legitimizing what is now done illegally, and yet it may also involve penalties that are stiffer than what the pro-illegal-immigration crowd would be willing to accept.
While I will never play an economist (even on TV), mutual economic incentives always seem like a good idea to me.
Of course, going to war over the issue is also a severe form of "tax" for border violations. The Iran-Iraq war involved some border disputes...for example.