Audience members listen as President Obama speaks about the importance of education in providing skills for American workers during a visit Oct. 25 at Pathways in Technology Early College High School in Brooklyn, N.Y. (Seth Wenig/AP)

President Obama called Friday for “political courage in Washington” in a speech at an innovative public high school here, urging Congress to approve more money for education as a partisan debate over federal budget priorities is set to begin.

Sleeves rolled up and suit jacket off, Obama warned that the opportunities that were open to him as a young college student in New York are threatened by government spending cuts and a rapidly changing global economy.

Obama told students attending Pathways in Technology Early College High School, a government-
industry collaboration, that they are receiving the kind of math-and-science-heavy education essential for the next generation of workers.

But he also suggested that, while new education methods are being adopted here and across the country, government dysfunction is too often blocking spending that he said could expand programs vital to economic development efforts.

“We’ve got to have the courage to do it,” Obama told an audience of ebullient students, teachers and officials. “We also need some political courage in Washington. We don’t always see that.”

Obama’s appearance here, which came ahead of a pair of scheduled fundraising events, was designed to begin marking out his spending priorities before congressional leaders start budget negotiations next week. The out-of-town journey also came amid continued controversy in Washington over the bungled Web site launch of Obama’s signature health-care program.

Before arriving here Friday, Obama held a conference call with Senate Majority Leader Harry M. Reid (D-Nev.), House Minority Leader Nancy Pelosi (D-Calif.), Senate Budget Committee Chairman Patty Murray (D-Wash.) and House Budget Committee ranking Democrat Chris Van Hollen (Md.) to discuss his budget priorities ahead of the talks, White House officials said.

Obama’s visit was his first outside Washington since the government shutdown ended last week. In its aftermath, he has called for bipartisan cooperation to make the government work effectively and to repair the damage caused to the broader economy when it does not.

In the budget he proposed this year, Obama outlined cuts to entitlement programs, new spending on education, scientific research and transportation projects, and the end of certain tax breaks that benefit the wealthiest Americans. He reiterated those priorities in his speech here.

White House officials say Republicans and Democrats have an interest in replacing deep, across-the-board spending cuts, known as the sequester, with a negotiated budget.

But those officials also said the budget talks scheduled to conclude in mid-December, and a subsequent congressional vote, will determine how much either party is willing to disappoint its most loyal voters in exchange for compromise.

Obama visited this Brooklyn high school, known as P-Tech, to hold it up as an example of the innovative education program he believes the next generation of American jobs will demand. He proposed $300 million in his budget this year to better prepare high school students for college and a workforce being reshaped by technology, invention and the knowledge those require.

The school opened two years ago as a partnership between New York City’s public school system, the City University of New York and IBM to train high school students for technology jobs.

The school’s enrollment is open, and is expected to grow from 335 students to about 450 students by the beginning of the next school year. The curriculum runs for six years, after which students graduate with an associate degree in applied science from CUNY. Those who do are given priority for jobs at IBM.

The model is being tried in several places across the country and is expanding in New York.

Obama has framed the argument for more spending on education in terms of economic competitiveness in an increasingly crowded global marketplace for ideas and qualified workers.

“If you don’t have a good education, it is going to be hard for you to find a job that pays a living wage,” Obama said. “And, by the way, other countries know this.”

In an introduction, New York Mayor Michael R. Bloomberg (I) called P-Tech “one of the most innovative schools in America.”

“A high school diploma is no longer a ticket to the middle class,” Bloomberg said.

After his visit to the school, Obama met with Bloomberg’s likely replacement, Democratic mayoral candidate Bill de ­Blasio, at a famous Brooklyn eatery called Junior’s. “Do you know your next mayor here?” Obama asked patrons and employees before ordering two cheesecakes — one plain, one strawberry — to go.

“We’ll be eating it on Air Force One,” Obama told employees.