By Alister Bull and Patricia Zengerle

WASHINGTON (Reuters) - President Barack Obama on Tuesday offered modest steps to spur jobs and defended his push to get the U.S. economy growing, amid deep public dismay over double-digit unemployment that has eroded his popularity.

Obama proposed small business tax cuts and energy efficiency rebates -- a so-called cash-for-caulkers program -- to boost jobs, but gave no details on the cost of the action.

He also called for an extension of unemployment and health insurance benefits for the more than 15 million out-of-work Americans, and stressed that reducing the jobless rate was the best way to tackle the country's record deficit.

"There are those who claim we have to choose between paying down our deficits on the one hand, and investing in job creation and economic growth on the other. But this is a false choice," Obama said in a speech.

There was no immediate financial market reaction to his remarks, which had been broadly anticipated.

"He was trying to thread the needle between short-term stimulus and long-term fiscal responsibility, or deficit reduction," said Ted Gayer, a senior fellow at the Brookings Institution, where Obama spoke.

The White House must placate investors nervous about deficit spending with the political imperative of getting the jobless rate down.

U.S. unemployment dipped slightly to 10 percent last month. But Americans remain anxious about the economy, nudging Obama's approval ratings to 50 percent or below and potentially dimming his Democratic Party's prospects in midterm congressional elections next November.

A CNN/Opinion Research Corp. survey released on Tuesday found that American optimism on the economy is fading. Only 34 percent of those polled thought things were going well, down 3 percentage points since November.

"I voted for Obama last year, but I'm not sure I'd vote for the Democrats again next year," said Alicia Lockheart in Phoenix, Arizona.

She lost her job eight months ago and said she now gets by on food stamps and child support.

ORDINARY AMERICANS

Obama's speech was the latest effort to show that he is focused on the woes of ordinary Americans, and follows a White House jobs forum and visit last week to Allentown, Pennsylvania, in the industrial heartland.

It is vital for Obama to show Americans he is not getting distracted by other pressing issues like the war in Afghanistan and his effort to overhaul the healthcare system.

His remarks were also on the eve of a trip to Oslo, where Obama will accept the Nobel Peace Prize on Thursday, and a week before he attends a climate change summit in Copenhagen.