Salmonella outbreaks. E. coli outbreaks. Millions of dollars in economic losses.

These are among the scenarios the Obama administration warned about last month as it claimed the sequester would force the U.S. Department of Agriculture to furlough meat inspectors.

But while the administration prepares to take that step, it continues to pursue a "partnership" with the Mexican government to "raise awareness" about food stamps among immigrants from that country. When a top Senate Republican proposed cutting off funds for that program last week -- in the form of an amendment to a budget resolution -- Democrats on the Budget Committee shot it down.

It's hard to put a firm price on the cost of the partnership, which was launched under the George W. Bush administration. But an aide to Sen. Jeff Sessions, R-Ala., who has railed against the partnership for months, said it could easily be in the millions. Since 2004, the program has blossomed to include dozens of meetings and conferences and health fairs with Mexican officials -- all of which cost money, not to mention the cost to the food stamp program of new enrollees brought in as a result of this partnership.

Sessions, in a statement to FoxNews.com, said he believes the public will eventually demand an end to the program, though the Senate Budget Committee allowed it to continue in the vote last week.

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"We have uncovered extensive evidence that federal authorities have -- during the Bush and Obama administrations -- aggressively undermined a core legal tenet of immigration policy: that those granted admission should be self-sufficient and contribute to the economic health of the nation," Sessions said. "It is amazing that Budget Committee Democrats would unanimously vote to continue funding these costly promotions, especially when our debt is causing such profound economic harm."

According to a letter from Agriculture Secretary Tom Vilsack to Sessions last September, the "partnership" since 2004 has included roughly 91 meetings between U.S. and Mexico embassy and consulate staff; 29 health fair events; and 31 roundtable discussions, conferences and forums in 20 cities.

Twenty percent of the meetings and activities occurred since 2008, according to Vilsack's letter. Sessions is concerned the collaboration amounts to a vehicle for the USDA to pressure people onto the food-stamp rolls -- in this case, noncitizen immigrants from Mexico.

The USDA denies this. In his letter last year, Vilsack said the purpose is "to help eligible people in need make informed decisions about whether or not to seek assistance."

The initiative is one of several the agency has "to promote awareness of nutrition assistance among those who need benefits and meet all program requirements under current law," Vilsack told Sessions in the 24-page letter.

However, his letter indicates the number of legal, noncitizens participating in the program -- now called the Supplemental Nutrition Assistance Program -- has increased from 425,000 to 1.23 million between 2001 and 2010.

Meanwhile, the USDA continues to press forward with plans to furlough meat inspectors, describing it as a necessity of the sequester -- though the department has eased off a bit on warnings that this could lead to more foodborne illness, since all meat and poultry will still have to be inspected.