This week, the Senate is to consider controversial legislation to overhaul U.S. immigration law. Competing reform proposals agree on the need to curb illegal immigration, but just how to accomplish that goal, and what should be done with the estimated 11 to 12 million illegal aliens in the United States, is provoking sharp debate.

Republican Senator Arlen Specter of Pennsylvania says immigration reform should be grounded in reality and practicality. Speaking on NBC's Meet the Press program, Specter said it is in America's interest to provide a vehicle for undocumented workers to legalize their status, and emerge from the shadows of society.

"If we do not have some realistic proposal to give them the opportunity to work lawfully, and, ultimately, to obtain citizenship, then they are going to be fugitives [in the country]," said Senator Specter.

But some legislators say illegal immigration is, by definition, a law enforcement matter. Republican Congressman James Sensenbrenner of Wisconsin spoke on NBC's Weekend Today program.

"We ought to do [border] enforcement first," said James Sensenbrenner. "Twenty years ago, we gave amnesty to illegal aliens. It did not solve the problem of more illegal aliens coming across the border. And, unless we enforce the law that makes it an offense for an employer to hire an illegal alien, and have border enforcement, we will just be encouraging more people to come here [illegally]."

Last December, the House of Representatives passed a bill that would massively expand U.S. border enforcement, compel employers to verify workers' citizenship, and make it a federal crime to provide assistance to undocumented aliens.

The bill has been referred to the Senate for consideration, but Massachusetts Senator Edward Kennedy says the proposal is flawed. Kennedy, a Democrat, spoke on the CBS program Face the Nation.

"We cannot solve the problem of illegal immigration by law enforcement alone," said Senator Kennedy. "We have spent $20 billion on chains and fences and border guards along the southern border in the last 10 years, and it does not work. What we need is a comprehensive approach."

And that approach, according to Kennedy, should be to include a means for undocumented workers to legalize their status.

But, speaking on Meet the Press, Colorado Republican Congressman Tom Tancredo argues such a plan would amount to a de facto amnesty for illegal aliens.

"The crime they have committed is coming into this country, without permission," said Tom Tancredo. "The penalty that is supposed to be applied under the law that we have today is deportation. If you say, 'you can come across the border, without our permission, and you will be able to stay' - it is amnesty. And what it does is send a horrible message."

Senator Specter disagrees.

"It is not amnesty," he said. "These undocumented aliens are going to have to pay a fine. They are going to have to work for six years to be on the citizenship path. They are going to have to go through a criminal, or background check. They are not going to go ahead of people who have been waiting in line for citizenship."

The immigration debate is revealing rifts within the Republican Party, which controls both houses of Congress.

President Bush has proposed creating a guest worker program that would match foreign laborers with U.S. employers, who are unable to fill positions through the domestic workforce.

Saturday, more than half a million immigration advocates marched though downtown Los Angeles to protest the attempts to make illegal immigration a felony. Similar demonstrations drew thousands of people in Denver, Phoenix, Milwaukee and Dallas.