Barack Obama has issued an impassioned appeal to disgruntled Democratic supporters, urging them to "wake up" and put aside their gripes about his leadership or risk a Republican backlash in the US midterm elections, now just six weeks away.

In a series of campaigning events on Monday night, a combative Obama turned his attention to one of the most dangerous aspects of the pending elections for his party: the possibility of a devastatingly low turnout among Democratic voters. He came face to face with the kind of disaffection now being vented by once loyal supporters.

An African American woman, Velma Hart, told him she had grown "exhausted of defending you, defending your administration, defending the mantle of change that I voted for, and deeply disappointed with where we are right now".

Obama deployed a carrot and stick approach at the three events – a televised town hall meeting and a fundraising dinner in Washington, and a speech to party members in Philadelphia. On the one hand he attempted to assuage Democratic doubts about his administration, but he then went on to berate leftwingers for their misguided criticism of him.

"When I hear Democrats griping and groaning and saying 'the healthcare plan didn't have a public option' … or, 'yes, you ended the war in Iraq, but you haven't completely finished the Afghan war yet', I say, 'folks, wake up'."

In Philadelphia, he said: "This is not some academic exercise. Don't compare us to the Almighty; compare us to the alternative."

Obama's outspoken tone – in contrast to the more measured approach he has taken for most of his 20 months in office – reflected both his exasperation with his detractors within his own party and the recognition of the frustration felt by many of the millions who lined up to vote for him in 2008. That frustration was vividly expressed by Hart.

Standing a few feet in front of the president, she delivered a swingeing assessment of the past two years, broadcast live on CNBC. "I voted for a man who said he was going to change things in a meaningful way for the middle class. And I'm waiting sir. I'm waiting. I don't feel it yet."

Obama replied: "Times are getting tough for everybody right now, so I understand your frustration."

Velma Hart delivered a swingeing assessment of the president's tenure just a few feet away from him. Photograph: Bob Blanken

The exchange of views neatly sums up the challenge facing the White House in the final six weeks of campaigning before the 2 November election. Recent polls suggest that this year Republicans are unusually fired up about the ballot, partly as a result of the hyperbolic activities of the Tea Party movement. Democratic supporters, by contrast, are looking more apathetic than at any time since 1994, when Bill Clinton's party took a drubbing and Newt Gingrich's Republicans wrestled back control of Congress.

Gallup's polling suggests that 54% of Republicans are paying attention to the pending elections, compared with 30% of Democrats. The figure for Democrats is far lower than that registered at the same stage in the past four midterms, indicating that Obama still has a great deal of work to do if he is to avoid a punitively low turnout.

Peter Brown, of the polling institute at Quinnipiac university, said past trends suggest three elements of American society tend to have particularly low turnouts in midterms: black people, Hispanics and the young. All three are key Democratic target groups. "Obama has got to get these groups to vote," Brown said. Jennifer Duffy, of the independent research body the Cook Political Report, said lethargy among Democratic voters was understandable. "They don't dislike Obama but they haven't seen their lives improve much since the economic crash."

Bill Clinton has also pleaded with Democrats not to let their anger impair their judgment. Speaking at his own philanthropic gathering in New York, the Clinton Global Initiative, he said anyone who fails to vote would be making a "horrible mistake". He said a no-vote would be "Newt Gingrich all over again", adding: "You'll get the exact result you don't want."

What Velma Hart said to Obama

"I am a chief financial officer for a veterans service organisation, AmVets, here in Washington. I'm also a mother, I'm a wife, I'm an American veteran, and I'm one of your middle-class Americans. And quite frankly, I'm exhausted. I'm exhausted of defending you, defending your administration, defending the mantle of change that I voted for – and deeply disappointed with where we are right now.

"I have been told that I voted for a man who said he was going to change things in a meaningful way for the middle class. I'm one of those people, and I'm waiting, sir. I'm waiting. I don't feel it yet. And I thought, while it wouldn't be in great measure, I would feel it in some small measure.

"I have two children in private school. And the financial recession has taken an enormous toll on my family. My husband and I joked for years that we thought we were well beyond the hot dogs and beans era of our lives. But quite frankly, it's starting to knock on our door and ring true that that might be where we're headed again.

"And quite frankly, Mr President, I need you to answer this honestly, is this my new reality?"