"Strange things can happen in an election like this if we're not working hard, if we're not engaged, if we're not participating," Obama told donors at a fundraiser for the Democratic National Committee.
"I want us to run scared the whole time," he said.
Obama decried the clashes between supporters of likely Republican presidential candidate Donald Trump and protesters on Thursday at a rally in San Jose, California.
"We saw in San Jose these protesters starting to pelt stuff at Trump supporters; that's not what our democracy's about," Obama said.
"There's no room for violence. There's no room for shouting. There's no room for a politics that fails to at least listen to the other side, even if you vehemently disagree," he said.
Obama spoke to about 90 people who paid $10,000 to $30,000 for the dinner at the home of Robert Rubenstein, a personal injury lawyer.
He noted the "constant" television coverage of Trump, saying "celebrity and fame is such a driver in this culture."
Obama said Republicans have "no coherent economic theory."
"Rather it is feeding resentments and looking for a 'they' to blame for whatever frustrations people understandably feel at any given point in time," he said.
"Being able to say it's immigrants or it's gays or it's somebody that is taking something away from you - that's the essence of the message that the Republican nominee is delivering," he said.