The border crisis involving unaccompanied children has pushed immigration suddenly to the top of the national agenda – and Americans have at least some consensus about what action Congress should take.

Though immigration reform proposals have struggled to find support in the Republican-controlled House, recent opinion polls show substantial support for its core planks. The polls suggest that, despite poisonous political rhetoric over immigration reform, there are bridges of agreement among Americans about the steps that should be taken – and frustration over Congress’s inability to act.

Specifically, the idea of tighter border security has strong majority support. So does the idea of providing for legal status – and possible paths to citizenship – for immigrants now in the US illegally.

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In a new survey released Thursday, the public also weighs in on the minors who have been flooding across the border this year – the trend that has pushed immigration to the forefront. In the new Pew Research Center poll, a slim majority favors expedited decisions on deportation or asylum for those minors.

Media images of the porous southern border and of a tide of children making the perilous journey from Central America have clearly had an impact on public opinion.

A monthly Gallup poll, released alongside the Pew survey Thursday, finds that Americans’ top national priorities have changed significantly since June. Immigration is named as the No. 1 national problem by 17 percent of respondents, up from 5 percent who said that in June and 3 percent in January – and higher than at any time since 2006.

That puts immigration at the top of the list in Gallup’s new results. It’s not that the economy is no longer a big worry. That issue would still rank as a bigger concern if you lump people who put “economy” first (15 percent of respondents) together with those who say “jobs” or “unemployment” (14 percent). Still, concern about those two categories fell in July even as immigration surged.

Concern about immigration spans all regions, but it was named as the top problem most often in the West (by 24 percent of those polled) and least often in the Midwest (by 13 percent). Some 23 percent of Republicans say it’s the top issue, compared with 16 percent of independents and 11 percent of Democrats.

On the question of what should be done, the nation still shows longstanding fault lines, with substantial numbers of Americans in both the “no-amnesty” and the “path to citizenship” camps.

A May New York Times poll hints at how immigration is central to a broader debate over America’s character as a nation. It found 54 percent agreeing with the idea that the nation should be “a country with a basic American culture and values that immigrants take on when they come here.”

But another 42 percent favored the ideal of “a country made up of many cultures and values that change as new people come here.”

As divisive as the issue is, public views also point toward some possible consensus solutions.

In the new Pew Research Center poll, for example, 68 percent of Americans support the idea that “immigrants living in the US who meet certain requirements should be allowed to stay in the US legally.” That total included majorities of both major political parties, and of political independents.

Support for legal status has sagged a bit as the border crisis has emerged in the news, however. Among Republicans, only 54 percent in July favored the “allowed to stay” option in the Pew poll, down from 64 percent in February.

For some years now, Americans have supported the general idea of a path to citizenship. As far back as 2006, two-thirds of Americans in a Los Angeles Times/Bloomberg poll supported such a path for illegal immigrants who learn English, pay a fine, and meet other requirements.

Many Americans want a tough-love approach. In a June Gallup poll, 63 percent said immigration is generally “a good thing” for the country, but more said the overall number of immigrants should be decreased (41 percent) than increased (22 percent).

And a Gallup poll last year found 83 percent support for a law “that would tighten US border security and provide the Border Patrol with increased technology, infrastructure and personnel.”

The new Pew poll bores in on the recent influx of minors. It finds 53 percent of Americans saying the legal process for dealing with Central American children who cross the border illegally should be accelerated, even if that means that some children who are eligible for asylum are deported.

Some 38 percent would rather stay with the current policy, even though the process could take a long time and the children will stay in the US in the interim.

Hispanic Americans in the poll were more evenly divided, with 47 percent saying “speed up the process” and 49 percent favoring the current policy.

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• Immigration Issues
• Politics & Government
• immigration reform