“We need a system that doesn’t just fix the problem for the 12 million people who might be here illegally, but that’s fair to the people who have been waiting in line for a long period of time and that’s fair to the American citizens who want our sovereignty protected,” said Labrador, who serves on the House Judiciary Committee’s immigration subcommittee.

Rep. Lamar Smith, R-Texas, criticized senators for promoting an “amnesty” plan that will only compound the problem by leading to more illegal immigration.

“When you legalize those who are in the country illegally, it costs taxpayers millions of dollars, costs American workers thousands of jobs and encourages more illegal immigration," Smith, a former chairman of the House Judiciary Committee and a member of the immigration subcommittee, said in a statement.

Most everyone agrees immigration reform is needed, according to Rosemary Jenks, director of government affairs for NumbersUSA, which advocates for greater enforcement. But the public is not ready for legislation that includes “meaningless enforcement measures,” she said.

It’s not just Obama’s policies and the Senate agreement that are effecting change for illegal immigrants.

Sharry of America’s Voice says the trend dates back to last summer, with the historic Supreme Court decision striking down much of Arizona’s controversial law.

The court upheld the “show me your papers” requirement mandating law enforcement officers to check the status of people stopped for various reasons who might appear to be in the U.S. illegally. But it threw out other provisions of the law, such as requiring immigrants to obtain or carry immigration registration papers. The decision was followed by Obama granting deferred action to hundreds of thousands of undocumented youth.

In last fall’s election, 71 percent of Latinos voted for an incumbent president who championed comprehensive legislation.

More local changes have followed. Illinois passed a law that allows illegal immigrants to get driver’s licenses. Lawmakers in Nevada and California are considering similar measures.

When Republicans in North Carolina put together a special committee on immigration, the expectation was they’d recommend state legislation along the lines of Arizona and Alabama.

But the special House panel disbanded abruptly last month without offering any recommendations other than calling for the federal government to do more.

Lesley Clark of the Washington Bureau contributed.