It isn't in the interest of the Mexican government to stem the flow - forget about all the remittances sent back by illegal aliens working in the US. More then anything, the open border serves as a relief valve, allowing them to offload the burden on Mexico's social services by anywhere from 8 to 17% of the Mexican population (depending on what figures you want to use). As the labor force began to peak a few years back as the result of the booming Mexican population, the US represented an outlet for unemployed people (the Mexican birth rate has plummeted in the last few years, but it will take years for the effects of this to be felt).
Mexico City has no reason to discourage cross-border crossings - it's a win-win situation, reducing excess labor, bringing capitol into the nation, and decreasing government expenditures. It's up to us to take care of the border, Mexico has no conceivable reason to do anything about it.