TUCSON, Arizona (CNN) -- President Bush launched a new push to crack down on illegal immigration from Mexico, promising to "harden" the southern U.S. border while reviving his proposal for a guest-worker program critics say is a form of amnesty."The American people should not have to choose between a welcoming society and a lawful society," Bush told an array of customs, immigration and border patrol officers at Davis-Monthan Air Force Base. "We can have both at the same time."After spending the Thanksgiving holiday with family at his Crawford, Texas, ranch, the president hit the road to sell his immigration policy, with a stop in El Paso, Texas, scheduled for Tuesday.Bush endorsed building more jail cells to hold those caught inside the United States illegally, speeding up deportations, cracking down on fraudulent papers and "hardening" the border with additional officers, fences and monitoring devices."Securing our border is essential to securing the homeland," he said.Bush also urged Congress to back his proposal for a temporary-worker program, a long-standing idea he said would match legal immigrants with employers "to fill jobs that Americans will not do." But he said the program would not provide a path to citizenship for those who entered the country illegally, saying that doing so would encourage other would-be migrants to cross the border."I support increasing the number of annual green cards that can lead to citizenship," Bush said. "But for the sake of justice and for the sake of border security, I'm not going to sign an immigration bill that includes amnesty."Bush also said he would crack down on U.S. businesses that hire illegal immigrants, saying American employers "have an obligation to abide by the law."The renewed focus on immigration follows a sharp drop in the president's approval rating, and recent polls indicate most of his fellow Republicans oppose his handling of the issue.Many of his conservative allies have criticized the guest-worker program, which they say would allow illegal immigrants to obtain legal status. Many Democrats have also opposed the proposal, which Bush first outlined in January 2004. (Full story)Rep. Tom Tancredo, an outspoken advocate of a tough stance on illegal immigration, said Bush's credibility "is on the line, big-time" over the issue."People even in his own party are worried about whether or not you can really take to the bank what he tells you," said the Colorado Republican. "So the president has not only got to actually say the right stuff, he's got to do the right stuff. We've got to see action on top of words."But one GOP analyst has warned that Bush must strike a delicate balance by talking tough on border security without alienating swing voters, women and Hispanics -- the latter a group Republicans have tried to court since Bush's first presidential campaign."Republicans are talking about solutions rather than just making a lot of noise," said Leslie Sanchez, the former director of Hispanic communications for the Republican National Committee. "But with those solutions come a lot of things that can look like immigrant-bashing."White House spokesman Scott McClellan said Bush wants a "comprehensive" overhaul of immigration policy, emphasizing both border security and the guest-worker proposal. But he denied that represented any shift in the president's focus.CNN's Elaine Quijano contributed to this report.