President Obama watches a project of seventh grade students at Mooresville Middle School in Mooresville,N.C., on June 6. (JEWEL SAMAD/AFP/Getty Images)

President Obama liked the idea laid out in a memo from his staff: an ambitious plan to expand high-speed Internet access in schools that would allow students to use digital notebooks and teachers to customize lessons like never before. Better yet, the president would not need Congress to approve it.

White House senior advisers have described the little-known proposal, announced earlier this summer under the name ConnectEd, as one of the biggest potential achievements of Obama’s second term.

There’s just one catch: The effort would cost billions of dollars, and Obama wants to pay for it by raising fees for mobile-phone users. Doing that relies on the Federal Communications Commission, an independent agency that has the power to approve or reject the plan.

Republicans vow to oppose any idea that raises costs for consumers, while others question whether it’s appropriate to use the FCC to fund an initiative that is better left to Congress’s authority.

“Most consumers would balk at higher costs, higher phone bills, and I sure hope that this is not part of the equation that ultimately comes out,” said Rep. Fred Upton (R-Mich.), chairman of the House Energy and Commerce Committee. “If they pursue that course, there’s going to be pushback, absolutely.”

Republicans said that if the proposal moves forward, they will hold congressional hearings and pressure the FCC to side against the plan, although it’s unclear how much they could do. There are five seats on the commission — two filled by Democrats, one by a Republican, and Obama has nominated candidates for two open spots. The commission has taken the initial steps in what could be a year-long process before it decides.

ConnectEd, which seeks to provide high-speed Internet service to 99 percent of schools within five years, is a case study in how Obama is trying to accomplish a second-term legacy despite Republican opposition in Congress.

“It’s got a lot of the characteristics of big-vision policy that you really don’t get through legislation anymore,” said Rob Nabors, White House deputy chief of staff, who is coordinating executive actions.

The proposal arrived at the White House after the 2012 election, when Education Secretary Arne Duncan and Julius Genachowski, a law school friend of Obama’s who was FCC chairman at the time, broached the idea.

Inside the White House, there was interest in the policy but concern about the politics.

The proposal makes use of the FCC’s ability to charge consumers fees to fund specific priorities, such as subsidizing phone service for the poor. The program, known as the universal service fund, has received bipartisan support in Congress but has drawn criticism from some telecom companies for raising fees and from some conservatives who oppose what they call handouts.

In the case of ConnectEd, White House officials worried that Obama could be accused of raising taxes on all Americans who use phone or Internet service, amid a broader debate in which Republicans are saying he is trying to raise taxes on the middle class. The cost for the initiative is estimated at $4 billion to $6 billion, and the administration said it could work out to about $12 in fees for every cellphone user over three years.

A senior administration official said that if the idea had come up during the presidential campaign, it probably would have been abandoned because of the political risk. Democrats faced withering critiques in the 1990s for advocating gas taxes to fund roads and bridges, and then-Vice President Al Gore was put on the defensive over the “Gore tax,” the 1996 law that gave the FCC the power to charge such fees.

White House officials were concerned about the perception that they would try to unduly influence the agency.

“Using the FCC as a way to get around Congress to spend money that Congress doesn’t have the political will to spend — I think that’s very scary,” said Harold Furchtgott-Roth, a Republican former FCC commissioner. “Constitutionally, it’s Congress that decides how federal funds should be spent.”

White House officials, led by National Economic Council Director Gene Sperling and Domestic Policy Council Director Cecilia Muñoz, weighed whether to embrace the policy, lend quiet support or just avoid it. White House Chief of Staff Denis McDonough concluded that Obama had to decide himself.

Sperling and Muñoz wrote a memo to the president explaining the idea and highlighting the political risks. Obama had long expressed frustration that countries such as South Korea had embraced technology in the classroom so much better than the United States had. He became enthralled with the idea and gave it the go-ahead.

“We are here to do big things — and we can do this without Congress,” he later told his staff in a meeting, an aide said.

Administrative officials argue that ConnectEd would foster a whole new educational ecosystem. “It creates a tipping point that leads to new forms of educational content, more affordable educational devices, more teachers being able to use alternative ongoing assessment tools, and kids able to work at their own pace and who can try and try at the privacy of their desks without having to feel embarrassed,” Sperling said.

But not everyone is convinced — including at the FCC, where one of the three sitting commissioners, Republican Ajit Pai, opposes increasing fees and has raised concerns about a one-size-fits-all solution, even as he has welcomed public comment on the initiative.

Pai noted in a recent speech that FCC programs that charge consumers to pay to wire schools and libraries have been beset by a wide range of problems and inefficiencies. “We shouldn’t force schools to skew their spending decisions in order to help us meet an arbitrary national target,” he said.

But Obama is pressing ahead. In June, to announce ConnectEd, he visited a school in Mooresville, N.C., that had used alternative sources of funding to expand broadband.

“How do we make sure Americans have the chance to earn the best skills and education possible?” the president asked a crowd of students and teachers. “At a moment when the rest of the world is trying to out-educate us, we’ve got to make sure that our young people — all you guys — have every tool that you need to go as far as your talents and your dreams and your ambitions and your hard work will take you.”

The announcement garnered little attention, despite the game-changing way the administration views the idea.

On the same day of Obama’s visit, news reports were dominated by details of a wide-ranging National Security Agency surveillance program that has since become one of the major controversies of the president’s second term.

As Air Force One flew toward North Carolina that day, Obama lamented to his education secretary that one of the administration’s biggest ideas was going to be overtaken by other news.

“I remember him sort of saying, ‘It’s a shame that there’s going to be a focus on the noise rather than something that’s real and meaningful,’ ” Duncan said.