WASHINGTON — Will 5 million undocumented immigrants start pushing U.S. citizens out of their jobs now? Will they start getting government benefits and draining city hall budgets? Or will they start moving up the ladder, paying taxes and giving a boost to the economy?

President Barack Obama’s decision to protect them from deportation and allow them to apply for work permits actually is likely to produce neither scenario. It packs little economic punch because the immigrants are already here and the reprieve is only temporary.

And since the executive order did not significantly ease the backlog of visa requests for high-skilled immigrants, the president’s action might actually be negative for the economy, because it appears to lessen the chance for a congressional compromise to allow in greater numbers of engineers, scientists and high-tech professionals.

“One more unfortunate consequence of this decision is that it will make it very difficult, if not impossible, to get a legislative solution to high-skilled immigration in the next two years,” said Robert Litan, an economist and senior fellow at the Brookings Institution, a center-left think tank.

That concern was echoed by Thomas Donohue, president of the U.S. Chamber of Commerce, who also worried that the partisan move could further hurt chances of a bipartisan agreement.

How many of the 4 million to 5 million unauthorized immigrants will actually come forward and ask the federal government to suspend deportation proceedings and simultaneously seek work permits is unclear. Past programs have seen 60 percent or more of eligible immigrants participate, according to the Obama administration.

The administration suggested the actions would help boost wages.

“By providing individuals with an opportunity to come out of the shadows and work legally, we will also help crack down on companies who hired undocumented workers, which undermines the wages of all workers, and ensure that individuals are playing by the rules and paying their fair share of taxes,” the administration said.

Asked during a briefing to quantify the economic benefit from Obama’s action, senior administration officials said only that it was positive.

“We will be taking a look at that,” said one senior official who spoke on condition of anonymity as a matter of policy.

Some experts think workers may not seek permits, and employers may choose not to hire workers because the work permits last only until a new administration takes office, and can be undone by presidential action.

“The reality is they’re not going to be able to come to their employer and say, ‘Mr. Obama said I can do this,’ ” said David Card, a labor economist and immigration expert at the University of California, Berkeley.

Card expected very little to change via executive order, in part because until Congress overhauls the immigration system, employers “don’t want to take the risk . . . they don’t know what’s going to happen.”

Many of the unauthorized immigrants affected by the executive order are working off the books, being paid under the table already or working with falsified documents.

Coming out of the shadows means workers will explicitly qualify for some local, state and federal benefits and services, more than offsetting their new tax contributions. Unauthorized immigrants do pay sales taxes on anything they purchase in a store or restaurant, but what that all adds up to no one knows for sure.

On the cost side, however, the Federation for American Immigration Reform, which opposes Obama’s executive order, estimated in 2010 that the annual cost of unauthorized immigration to taxpayers is about $113 billion. About $84 billion of that burden fell on the state and local level, $52 billion on public education alone.

The group does not have a current number, said spokesman Ira Mehlman, but it thinks the dynamic is unchanged. It considers the executive order a “magnet for expectations,” encouraging future generations to emigrate to the United States with the hope of eventually benefiting from suspended deportations.