WASHINGTON – Two Republican senators from states with large numbers of illegal immigrants introduced legislation yesterday that would funnel at least $5 billion into border enforcement and create a temporary-worker visa requiring foreigners to return to their home countries when their jobs ended.

The bill, sponsored by Senators Cornyn of Texas and Kyl of Arizona, would toughen penalties for employers who hire undocumented workers, reimburse states for the costs of holding illegal immigrants who commit crimes, and require the issuance of machine-readable, tamper-proof Social Security cards within a year.

Messrs. Kyl and Cornyn, whose home states stretch along 85% of the U.S.-Mexico border, timed their bill’s introduction to keep immigration on the front burner at a time when debate over a Supreme Court nominee threatens to overshadow other congressional business.

Reflecting the political reality of their states, where frustration with the lack of border security runs high, the senators positioned their effort as a “workable and enforceable” solution – a phrase that hinted at the political balancing act they aimed to strike between plugging the nation’s porous border while still maintaining a flow of workers to businesses hungry for cheap labor.

The immigration issue, which President Bush has said is a priority for his second term, is a divisive one for the GOP. Many business-oriented Republicans want to ensure continued access to immigrant workers, while large numbers of social conservatives are angered by the ease with which illegal immigrants evade American laws.

The Kyl-Cornyn bill is the latest entry in a crowded field that includes legislation introduced in May by Senators Kennedy, a Democrat of Massachusetts, and McCain, a Republican of Arizona, and a bill introduced Monday by Rep. Tom Tancredo, a Republican of Colorado.

The Kennedy-McCain bill would create a new visa category that would not tie temporary workers to one particular job and would allow them to apply for permanent residence.

Mr. Tancredo’s legislation would make it a felony to enter American illegally and require the Department of Homeland Security to secure the border before a single worker legally could enter the country.

In what is perhaps an attempt to stake out the middle ground, the Kyl-Cornyn bill would:

* Require that all immigrants be registered, fingerprinted, and checked against criminal and terrorist watch lists.

* Allow immigrants to come for two years under the new temporary worker visas, after which they must return home for a year. They may apply for such a visa three times, for a maximum stay of six years.

* Oblige undocumented immigrants currently in America to register for a “mandatory departure” program that would give them time to leave voluntarily. They could re-enter through the temporary-worker program, but could not apply for permanent residence while in the United States.

* Enact enforcement and immigration measures at the same time in a “thoroughly overlapping” manner.

“Beyond the notion of returning the rule of law to the border, the single most important aspect of this bill is that it does not reward those who have broken the law and does not constitute an amnesty,” Mr. Kyl said.

The bill’s introduction comes less than a week after Homeland Security Secretary Chertoff called for an expanded guest-worker program and increased border enforcement as part of an overhaul of his department.

Messrs. Cornyn and Kyl, who said they consulted with the White House while drafting the legislation, described the estimated 10 to 11 million undocumented immigrants in America as the “thorniest problem of all.” They said they were committed to bringing those people “out of the shadows,” but it was unclear how this would work.

“Asking the 11 million illegal immigrants in this country to return to their home countries to live is a nonstarter,” said Tamar Jacoby, a senior fellow at the Manhattan Institute in New York City. “If what Senators Cornyn and Kyl mean is that some of them might have to go home to get processed so that they can return with green cards (signifying permanent-resident status), that might – emphasis on ‘might’ – be something you could get people to sign up for.”

Despite the senators’ tough talk, there was criticism among pro-enforcement conservatives that the bill was too permissive. Rep. Lamar Smith, a Republican of Texas, said that allowing temporary workers into the country would depress wages for American residents. He added that guest-worker programs could provide a venue through which terrorists could enter the country.

“Guest-worker programs sound good, but they only compound the already serious troubles that illegal immigration causes,” Mr. Smith said.