Amid a struggling economy and high unemployment, President Barack Obama met Thursday night with a small, elite group of Silicon Valley business leaders to sound them out on his economic policies.

The president’s plane touched down at San Francisco International Airport at 5:40 p.m., where he sprinted off the plane and was greeted by Lt. Gov. Gavin Newsom, Attorney General Kamala Harris, San Francisco Mayor Edwin Lee. He then posed for pictures with supporters before bounding onto a helicopter for a short flight to Cañada Community College in Redwood City.

Later, the president’s motorcade arrived in tony downtown Woodside, where crowds gathered to cheer him on before he met with 12 tech executives for a private 90-minute dinner at the home of prominent Silicon Valley venture capitalist John Doerr — a big campaign donor.

Those invited included Apple CEO Steve Jobs, Facebook CEO Mark Zuckerberg, Oracle CEO Larry Ellison, Google CEO Eric Schmidt and Twitter CEO Dick Costolo. White House officials confirmed all those on the guest list were present.

“The president specifically discussed his proposals to invest in research and development and expand incentives for companies to grow and hire,” White House spokesman Jay Carney said.

The president planned to leave the Bay Area on Friday morning and travel to Hillsboro, Ore., where Intel CEO Paul Otellini is scheduled to give him a tour of the world’s most sophisticated chip-fabrication facility. Obama also will review the Santa Clara chip-maker’s programs to advance science, math and engineering among students across the country.

Obama, who is working to smooth out a rocky relationship with the U.S. Chamber of Commerce, has had much warmer relations with many valley tech leaders. In October, he attended a fundraiser at the home of Google executive Marissa Mayer after meeting with Jobs for 45 minutes at the Westin Hotel in Millbrae. Schmidt, an informal adviser to the president, campaigned for Obama in 2008.

“The chamber in some respects represents the old guard — the Procter & Gambles, the Fords, the DuPonts,” said Larry Gerston, professor of political science at San Jose State. “But when you are talking about innovation of the 21st century, that’s where you get into the Googles, the Facebooks, the Apples and the Genentechs. If you look at the Obama view of the world — it’s high-speed trains, it’s broadband.”

Google and Oracle ranked among the top 10 spending lobbyists in the computer industry last year, according to the Center for Responsive Politics. Google, which ranked third, spent $5.1 million on lobbying last year while Oracle ranked fourth with $4.8 million.

Gerston, who called Thursday’s gathering a “study session,” predicted Obama would do more listening than talking with the leaders of companies around the table, who are hiring by the thousands.

“Of the 66,000 jobs added in California last year, 12,000 — 18 percent — came from Silicon Valley, which has less than 5 percent of the state’s population,” he said.

And talking tech with the likes of Jobs and Zuckerberg is good for the BlackBerry-toting president’s image, Democratic political consultant Jude Barry said.

“Obama is better off embracing Silicon Valley than other elements of American business,” he said. “Americans don’t blame Google and Facebook for losing their homes.”

But Orson Aguilar, executive director of the Berkeley-based Greenlining Institute, a multiethnic public policy group, took aim at Obama for “schmoozing wealthy tech moguls” while his 2012 budget proposal calls for cuts in social programs.

“He shouldn’t be calling it a job-creation event,” Aguilar said. “It’s insulting. To spend all that money to meet with billionaires in a mansion is not a good use of our taxpayers’ dollars. We’d prefer he was spending time with those who have been suffering from the lingering effects of the economy.”

And the Republican Party of California called the president’s West Coast trip a “re-election campaign photo op.”

Closed-door meetings can be a lot more productive than those played out in front of the media, said Betsy Mullins, vice president of policy and political affairs at the Silicon Valley lobbying group Tech Net. She worked as a senior adviser to Energy Secretary Bill Richardson in the Clinton administration.

“Hearing from people who are actually creating jobs and growing the economy is a good reality check,” Mullins said. “These events are some of the most important things elected officials can do. You can dive into background when you don’t have a million eyes watching you. It’s a much more comfortable situation.”

All who attended the dinner, with the exception of Costolo, belong to TechNet.org, a 14-year-old technology lobbying group founded in Silicon Valley. And several of those have given campaign contributions totalling more than $900,000 to Obama and congressional candidates. Doerr and his wife have contributed more than $300,000 to candidates, with the lion’s share of their donations going to Democrats, according to campaign disclosure forms.

Obama was apt to hear support for some aspects of his proposed $3.73 trillion fiscal-year 2012 budget. The budget outlines more than $1 trillion in deficit reductions over a 10-year period — 75 percent from spending cuts and the balance from tax increases or the elimination of existing tax breaks.

Obama would also increase funding for the Department of Education to improve student competitiveness, make permanent the research and development tax credit and spend $148 billion in federal research, including $32 billion for the National Institutes of Health — initiatives sure to find backing in some valley boardrooms.

Contact John Boudreau at 408-278-3496.