Democratic lawmakers must soon decide whether President Barack Obama is leading them toward statesmanlike courage or political folly with his take-no-prisoners reassertion of an ambitious social agenda.

Obama used his first State of the Union speech Wednesday to push nervous Democrats to forge ahead on health care, despite voters’ worries and opposition from newly strengthened Republicans. Sharpening his focus on the economy, he offered a hodgepodge of tax breaks and other incentives to create new jobs.

For Republicans, Obama blended a mix of overtures and digs. But he mainly addressed fellow Democrats, who still can enact his agenda if they overcome fears fueled by events such as last week’s stunning GOP victory in the Massachusetts Senate race.

That setback may have cost Democrats their filibuster-proof Senate majority, Obama said, but “we still have the largest majority in decades, and the people expect us to solve some problems, not run for the hills.”

He accepted partial blame for the deep troubles facing his health-care push, but he implored lawmakers to finish the task rather than yield to public opposition.

“The longer it was debated, the more skeptical people became,” Obama told the joint session of Congress and a nationwide TV audience.

But health-care problems will continue for millions, he said, and “I will not walk away from these Americans, and neither should the people in this chamber.”

House and Senate Democratic leaders are scrambling to see if they can salvage the ambitious health-care package, which Republicans almost universally oppose. Obama’s pep talk was a call to arms, but he offered no new strategies for overcoming the steep parliamentary and political hurdles they face.

The president devoted most of his 65-minute speech to job-creation proposals, such as eliminating capital gains taxes on small business investment and extending tax breaks for businesses to invest in new plants and equipment.

But those proposals also face uncertainty in Congress, where Senate Democrats say they may need a piecemeal approach to win enough votes.

Obama said Republicans share a responsibility for governing, and he proposed meeting with their House and Senate leaders monthly. But his olive branch seemed brittle at times.

Without naming George W. Bush, he pointedly noted the previous administration left him a big deficit and a deeply troubled economy.

For good measure, Obama said the United States killed more al-Qaida terrorists in 2009 than in 2008.

Obama rebuked the Supreme Court for a recent decision that “reversed a century of law to open the floodgates for special interests” and foreign corporations to make unlimited campaign contributions.

At that, conservative Supreme Court Justice Samuel Alito made a dismissive face, shook his head in disagreement and seemed to mouth the words “not true” as the president spoke.

Republicans in the House chamber generally greeted such remarks with stony gazes and smirks.

The statements they issued as soon as Obama finished — or even before he finished, in some cases — were equally icy.

“We had hoped to hear a new commitment to keep his promises to govern from the center, change the tone in Washington, and work with both parties in a bipartisan way to help small businesses create jobs and get our economy moving again,” said House Republican Leader John Boehner of Ohio. “Unfortunately, the president and the Democrats in charge of Congress still aren’t listening to the American people.”