Facing recession-weary audiences across the country, President Obama frequently highlighted the possibilities of job training for the unemployed.

The new fields of green technology, advanced manufacturing or clean energy would require new skills that job training programs could provide. More education would bolster the workforce and the economy. And at a community college “summit” in October, Obama touted the colleges’ role in providing workers with skills to take advantage of new opportunities.

“These are places where workers can gain new skills to move up in their careers,” he said. “These are places where anyone with a desire to learn and to grow can take a chance on a brighter future for themselves and their families.”

But details of the budget compromise this week between the president and congressional leaders show federal funding for job training programs has taken a significant hit — more than $870 million in all. Included are cuts to occupational training grants at community colleges, green jobs classes and a program to help low-income older people acquire work skills.

While some liberal groups decried the reductions, they noted that the budget deal essentially fended off much deeper cuts to job training programs proposed by Republicans.

“It’s substantially better than what the House had proposed,” said Steve Savner, policy director for the Center for Community Change. But the cuts are still “significant and troublesome,” he said.

The move comes amid some doubts about the effectiveness of the programs, however. In January, a report from the Government Accountability Office noted that funding for federal employment and training programs had gone up $5 billion, to $18 billion, between 2003 and 2009.

“Little is known about the effectiveness of most programs,” it said, while noting that some of them overlapped.

Congressional critics of such programs seized on the report to argue they should be dismantled.

Even some Democrats profess doubts about their effectiveness.

“Are job training programs a good thing? Yes. Is it God’s gift to workers? No,” said Gordon Lafer, a Democrat who is a professor at the University of Oregon and author of a book, “The Job Training Charade.” “Much more important than training is creating jobs.”

Advocates of the programs note that it is difficult to measure their effectiveness because it requires tracking over long periods of time and sophisticated analysis to determine what role the job training had in students getting jobs and what role other factors, such as innate intelligence, have.

Advocates point to the specific programs and the help they provide to students.

Among the cuts made in the budget deal: A green jobs program took a $40 million hit; a program to get ex-offenders into the workforce lost $23 million; and another to help disadvantaged youths get high school diplomas and job skills lost $20 million.

The budget plan eliminated a $125 million grant program that allowed community colleges and other groups to run job training programs. Last year, for example, Salt Lake Community College had received $2.7 million from the program to create a center for training in new communications media; St. Johns River State College in Florida received $1.9 million for training for nursing and other health-care jobs; and Vincennes University in Indiana received $1 million to give students construction trade skills.

The largest single cut came from a program that helps low-income older people get training. Its budget was reduced by 45 percent, or $376 million.

“At a time of record unemployment and hardship among the elderly poor, [these] cuts will deal a terrible blow to these older workers,” AARP Foundation President Jo Ann Jenkins said in an e-mail. “No other programs, public or private, exist to pick up the slack when [these] cuts begin.”