President Obama's promised executive order to raise the minimum wage for government contract workers would likely affect less than half a million people and may face legal challenge.

What Obama is hoping is that his relatively narrow move will spur Congress to follow suit for all low-wage workers in the country.

The announcement came Tuesday after months of pressure from liberals, who worry that Congress will not move quickly, if at all, on legislation to gradually raise the federal minimum wage across the board to $10.10 an hour from $7.25.

Obama reiterated his support for that proposal during his State of the Union address on Tuesday, noting that it would help millions more than his executive order.

Related: Obama's economy in 17 charts

The president's executive order would effectively require businesses awarded new federal contracts for services or construction to pay their "federally funded" workers a minimum of $10.10 an hour.

The order likely could also apply to contract renewals, if a contract's legal terms are changed, noted Amy Traub, a senior policy analysts at the liberal think tank Demos.

According to estimates by Demos, Obama's order could help "hundreds of thousands" of workers, although fewer than 500,000 overall.

Plenty of details are unclear, however. Such as when workers would actually see higher paychecks. But there's a good chance it could take awhile.

The White House has said contractors would have to start paying a higher minimum by "the effective date of the order, so contractors will have time to prepare and price their bids accordingly."

But it could take a year or two just for the executive order to be implemented, said Daniel Gordon, a government contracts expert who oversaw federal procurement policy for the White House from 2009 to 2011.

In the meantime, Obama could face legal challenges to his executive order.

Related: What's my real living wage?

Advocates for a higher minimum wage note that an increase could lift low-wage workers above the poverty line. Obama hit on that message again on Tuesday. "[I]f you cook our troops' meals or wash their dishes, you shouldn't have to live in poverty," he said in his address.

The White House also argues that it makes good business sense for Uncle Sam and taxpayers.

"Boosting wages will lower turnover and increase morale, and will lead to higher productivity overall," the White House said in advance of the speech. "Raising wages for those at the bottom will improve the quality and efficiency of services provided to the government."

If challenged, Gordon said, Obama "will need to point to support for the proposition that paying the currently required minimum wage is causing a widespread problem of inefficiency," such as staff turnover.

Gordon, who said he personally supports an overall higher minimum wage, said concerns about turnover, productivity and morale may apply to some contracts in specific sectors. But he added it might be harder to show a widespread problem of inefficiency to justify a blanket increase.