President George W Bush has begun touring US states to rally support for his strategy to control immigration.
Many Mexicans try to cross the border with the US in search of a job
Mr Bush wants tighter security along the Mexican frontier, but he also plans to allow migrants with a job offer to stay in the US temporarily.
Some of his own supporters resist the so-called guest-worker plan.
"The programme... would not create an automatic path to citizenship. It wouldn't provide amnesty," Mr Bush told border officials in Tucson, Arizona.
"This programme would help meet the demand of a growing economy, and it would allow honest workers to provide for their families while respecting the law," he said.
Under his plan, undocumented aliens would be allowed to get three-year work visas.
They could extend them for an additional three years, under the condition that they would return to their home countries for a year to apply for a new work permit.
Some Republicans say Mr Bush's ideas would reward illegal immigration.
Others think the border would still not be secure enough to keep out terrorists and drug-traffickers.
About 10 million Mexicans live in the US and more than four million are said to stay illegally.
Mr Bush is also expected to visit the city of El Paso, Texas.