UK’s message to immigrants: Stay out

“It’s good for our economy, it’s good for our security, it’s good for our people and we should do it this year,” he said.

But don’t expect a bill to sail through Congress that easily, a senior House GOP leadership aide told CNN.

“Expectations are low” that any immigration bill could pass this year, the aide said. “There is a sincere desire to work on this issue, but there’s also very little good will after the President spent the last two months refusing to work with us.”

Republican lawmakers have said that they prefer reform on a piecemeal basis and that border security measures must be put in place before the status of undocumented immigrants can be discussed.

Obama lauded the Senate’s immigration bill, but House Majority Leader Eric Cantor has already said that the House won’t do anything with it because the GOP opposes it.

“I expect us to move forward this year in trying to address reform and what is broken about our system,” he said.

A CBS News poll released Wednesday found public support for immigration reform.

There is widespread support for providing a path to citizenship for undocumented immigrants if they meet certain requirements, including undergoing a waiting period, paying fines and back taxes, passing criminal background checks and learning English, the poll found.

The same poll, however, found that more people think that securing the country’s borders should be a priority over resolving the status of undocumented immigrants.

“It doesn’t make sense to have 11 million people who are in this country illegally without any … way to come out of the shadows, get right with the law, meet their responsibility and permit their families, then, to move ahead,” Obama said.

House Democrats introduced their own version of an immigration bill at the beginning of the month, one without the huge expansion of the Border Patrol included in the Senate bill.

One of the most contentious parts of the Senate version was a one-year path to citizenship for undocumented immigrants. Many Republicans have rejected any route to legal status as amnesty for lawbreakers.

Opinion: Immigration reform would help GOP

CNN’s Kevin Bohn and Bryan Koenig contributed to this report.