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“It’s true that immigration isn’t the No. 1 issue for Latinos but it became a kind of focal point for a president who made big promises [but] delivered record deportations,” Mr. Sharry said. “That all changed last Friday. He put major skin in the game.”

Immigration has proved a nettlesome issue for the past decade as first President George W. Bush and then Mr. Obama failed to build successful coalitions in Congress.

But with Hispanics playing an ever-larger role in presidential politics, the issue’s time may have come. Hispanics make up a significant chunk of voters in swing states such as Nevada, Florida and Colorado.

Early polling suggests as many as two-thirds of voters support Mr. Obama’s move, and it has energized Hispanic voters.

Some congressional Republicans are pushing back, saying the halt in deportations opens the door to fraud and goes beyond the president’s powers.

On Wednesday House Judiciary Committee Chairman Lamar Smith, Texas Republican, wrote asking whether the Justice Department has produced any new legal opinion to back up the president’s claim of authority.

“The American people and Congress have a right to know what your legal justification is for engaging in an action that a little over one year ago you believed was beyond the scope of the authority of the executive branch,” Mr. Smith said.

Still, Mr. Obama and his aides will have plenty of chances to take victory laps before major Hispanic audiences.

Next week the League of United Latin American Citizens (LULAC) holds its conference in Orlando, and next month the National Council of La Raza, the biggest Hispanic umbrella group in the country, holds its conference in Las Vegas.

In 2008 Mr. Obama and Republicans’ nominee, Sen. John McCain, spoke at all three. In fact, the NCLR conference in San Diego was where Mr. Obama made his campaign pledge to write an immigration bill.

This year Mr. Obama and Mr. Romney have only committed to NALEO.

Mr. Romney has declined LULAC’s invitation, and Mr. Obama is sending Attorney General Eric H. Holder Jr. and other officials in his stead.

NCLR is still awaiting answers for its invitations, but analysts said they’d be surprised if either man attends.