These are the results of a Zogby poll from 2002. Many of the links about the poll have since vanished, so I'll reprint the results here.

The original page at the group that commissioned it is archived at [1].

From [2]:

Zogby International conducted interviews of 801 adults chosen at random throughout Mexico, from Friday, May 25 to Saturday, May 26, 2002. Slight weights were applied to age and education to more accurately reflect the population. The survey has a margin of sampling error of +/- 3.5%. Margins of error are higher among sub-groups.

POLL QUESTIONS

Do you agree or disagree that the territory of the United States' Southwest rightfully belongs to Mexico?

Agree 58%
Disagree 28%
Not sure/Don't know 14%

By two to one, more Mexican respondents agree (58%) than disagree (28%) that the territory of the United States' Southwest rightfully belongs to Mexico. One in seven (14%) is not sure.

Do you agree or disagree that Mexicans should have the right to enter the U.S. without U.S. permission?

Agree 57%
Disagree 35%
Not sure/Don't know 7

A press release from the organization that commissioned the poll is at [3]:

Americans and Mexicans have widely divergent views of border issues, according to a new poll by Zogby International.

Zogby found that a large majority of the Mexican population believes the southwest territory of the U.S. rightfully belongs to Mexico, and that Mexicans should have the right to enter the U.S. without first obtaining U.S. permission.

By contrast, Zogby's survey of Americans conducted within a few days of the Mexican poll shows a large majority supports reducing immigration levels and wants the military deployed along the border to protect the U.S. from illegal immigration.

Zogby's poll found that 58 percent of Mexicans agree with the statement, "the territory of the United States' Southwest rightfully belongs to Mexico." Only 28 percent disagree, and 14 percent are unsure.

A similar majority, 57 percent, agree with the statement, "Mexicans should have the right to enter the U.S. without U.S. permission," while 35 percent disagree. Seven percent are unsure.

The survey has a margin of error of 3.5 percent. The Mexico portion of the survey was conducted in Spanish between May 25 and May 26 among 801 adults chosen at random throughout Mexico. The poll was commissioned by Americans for Immigration Control, Inc. (AIC), which advocates increased restrictions on immigration.

"There is obviously a large and significant gap between the attitudes of Americans and Mexicans," said Robert Goldsborough, AIC president. "While most Americans want immigration reduced, most Mexicans think they don't even need permission to enter our country. The poll clearly shows there is less common ground for immigration negotiations between Mexico and the U.S. than the leaders think. Support for a porous border and a loose migration policy occurs only on the Mexican side, not in the U.S."

Zogby's survey of American attitudes found wide majorities of Americans also oppose amnesty for illegal aliens. The U.S. portion of the survey was conducted of 1,015 likely voters in the U.S. from May 28 to May 30. It found that 65 percent disagree with the statement, "foreigners residing illegally in the U.S. should be given amnesty." Just 26 percent of likely voters support amnesty for illegals, while 9 percent are unsure.

A large majority, 58 percent, agree that the U.S. should "admit fewer immigrants each year." Only 6 percent want "more immigrants each year," and 30 percent want to "keep immigration at the current annual levels."

The single largest majority in the entire poll was found among Americans supporting use of the military to guard the border. Fully 68 percent of those surveyed agree with the statement, "the U.S. should deploy military troops on the border as a temporary measure to help the U.S. Border Patrol curb illegal immigration." Only 28 percent disagree, and 3 percent are unsure.

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[1] web.archive . org/web/20070208234453/http://www.immigrationcontrol.com/AIC_Zogby_Mexican_Poll.htm
[2] cairco . org/issues/citizenship-and-dual-nationality
[3] freerepublic . com/focus/news/713048/posts