Republicans responded that Mr. Obama's first step in the rancorous immigration debate must be to secure the border.
In a speech pushing for change in the system, Mr. Obama advocated a comprehensive approach that would insist the government, businesses and illegal immigrants themselves live up to their responsibilities within the law. Focusing on a "border security first" approach would fail, he said, because the system is too big to be fixed "only with fences and border patrols."
Obama also wants to create a pathway to citizenship for the estimated 11 million illegal immigrants in the United States; critics call that amnesty, which Obama denies because he would ensure that immigrants must first acknowledge that they had broken the law, pay fines and back taxes, perform community service and learn English.
Even in an election year battered by war and drenched in oil, it's the relentless flow of illegal immigrants crossing our southern border illegally that has turned out to be the politically charged third rail that politicians touch at their peril, reports CBS News correspondent Bill Whitaker.
Without setting a timeline, Mr. Obama questioned whether the political will exists to get a bill through Congress.
"Reform that brings accountability to our immigration system cannot pass without Republican votes," he said. "That is the political and mathematical reality." In the Senate, Obama's Democrats fall just short of the 60-vote supermajority needed to overcome Republican delaying tactics.
The leader of the Senate's majority Democrats, Sen. Harry Reid, is in a tight re-election race in Nevada, where 25 percent of the residents are Hispanic. Reid could benefit politically from enacting a broad immigration overhaul before November's congressional elections. He said he was committed to passing a bill this year.
The minority leader, Sen. Mitch McConnell, said Obama would get the bipartisan support he wants "if he would take amnesty off the table and make a real commitment to border and interior security."
Many immigrant advocates praised the president's comments. They had been pressing him for some time to give such a speech. Even though it broke no new ground, supporters said the speech would demonstrate Obama's commitment to an issue he promised would be a priority during his first year in office.
An organization of Hispanic conservatives, however, criticized the speech as a "sheer political move" ahead of the November congressional elections. Obama was elected with strong backing from Hispanics, and they could tip the balance in several tight races this year.
"President Obama is operating under the false assumption that Latinos are natural-born Democrats who will rally behind his policies in lockstep," said Alfonso Aguilar, executive director of the Latino Partnership for Conservative Principles. "Latinos must not let themselves be deceived by the soaring rhetoric that has replaced meaningful action on immigration."
In Arizona, which is weeks away from enacting a controversial anti-immigrant law that Obama has called "misguided," Republican state Rep. John Kavanagh said he was offended by the president's speech and comments about the new state law.
In the speech, Obama said the law is an understandable expression of the public's frustration with the government's failure to overhaul the immigration system, but it also is ill-conceived, divisive and would put undue pressure on local police departments.
The law requires police enforcing other laws to ask about a suspect's immigration status if there is reason to believe that the person was in the United States illegally. Immigrant advocates want the Justice Department, which is reviewing the law, to sue Arizona to block it from taking effect this month.
"There is deep-seated anger in the Latino community about what's going on in Arizona," Thomas Saenz, president of the Mexican-American Legal Defense and Education Fund, told CBS News.
Latinos make up 12 percent of the Arizona electorate and are central to Obama's political coalition. Anger at the GOP won't necessarily translate to votes for Democrats.
"At this point I think that both parties have real reason to be concerned," said Saenz.