"Executive order" was the rallying cry at a separate Democratic fundraiser Monday. Obama, the former instructor in constitutional law, responded to the criticism with a brief lesson in the nation's rules.
"If, in fact, I could solve all these problems without passing laws in Congress, then I would do so," Obama told the first group. "But we're also a nation of laws. That's part of our tradition. And so the easy way out is to try to yell and pretend like I can do something by violating our laws."
House Republican leaders have rejected the Democratic-controlled Senate's comprehensive immigration bill, which passed on a bipartisan vote in June. The far-reaching measure would provide new visa and workplace enforcement programs and billions of dollars for border security, along with a path to citizenship for millions.
Small, stand-alone bills from the House Judiciary Committee have languished for months, and leaders signaled that votes are unlikely in this year's remaining legislative days even though Obama recently embraced the piecemeal approach. Prospects for immigration legislation in 2014, with congressional elections looming, are slim despite the issue's political drag on the Republicans.
In the 2012 election, Hispanic and Asian Americans went overwhelmingly for Obama and Republican strategists know they need to make some inroads with these groups if they want to take the White House in 2016.
Advocacy groups have been as loud as the California protesters in calling for Obama to act while they maintain pressure on House Republicans with protests and acts of civil disobedience.
"House Republicans are infuriating, and legislation is the permanent solution, and we're going to keep fighting for legislation. But that doesn't let Obama off the hook," Frank Sharry, executive director of America's Voice, a pro-immigrant group, said Tuesday. "He continues to be the president who presides over record deportation."
What angers the advocacy groups is that many of those deported are immigrants who would qualify for legal status or citizenship under the Senate-passed legislation, which Obama supports.
Traveling with Obama in California, a White House spokesman, Josh Earnest, did not rule out some sort of executive action. That possibility unnerves Republicans who point to Obama's unilateral changes to the health care law, such as delaying some requirements and enrollment deadlines.
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Associated Press writer Alicia A. Caldwell contributed to this report.