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Hispanic voters are a key voter bloc as Mr. Obama seeks re-election next year, but many of them felt he broke his promise to them to work on legislation once he took office. Thursday’s move already was paying dividends as Hispanic advocacy groups praised the steps.

“After more than two years of struggle, demonstrations, direct actions and other activities, the administration has signaled that they are capable of delivering direct relief for immigrant families,” said Casa de Maryland, a pro-immigrant group. “We eagerly await confirmation from community members that their families can now expect to remain together.”

Two years ago, some staffers at U.S. Citizenship and Immigration Services had prepared a draft memo arguing that the administration retained broad powers that could serve “as a non-legislative version of ‘amnesty.’ “

But agency leaders and others in the administration had argued that the memo was inaccurate.

It was unclear Thursday how many people might be affected by the new rules. Pressure groups said up to 300,000 people could be eligible. In fiscal year 2010 alone, the government deported nearly 200,000 illegal immigrants who it said did not have criminal records.

Given the case-by-case basis of Thursday’s announcement, though, the groups said the actual number of people allowed to stay could be far lower.

In June, U.S. Immigration and Customs Enforcement, the agency that handles interior immigration law enforcement, issued guidance expanding authority to decline to prosecute illegal immigrants. The goal, ICE leaders said, was to focus on catching illegal immigrants who have committed other crimes or are part of gangs.

The chief beneficiaries of the guidance are likely to be immigrant students who would have been eligible for legal status under the Dream Act, which stalled in Congress last year.

Senate Majority Leader Harry Reid, Nevada Democrat, who asked Homeland Security this year to exempt illegal-immigrant students from deportation, said the move will free up immigration courts to handle cases involving serious criminals.