First lady Michelle Obama declared Tuesday that her husband’s record in office has proved his values, his vision and his courage, as the Democrats opened their convention here with a wide-ranging appeal to the diverse constituencies and interests they must bring out in force to reelect the president.

The first night of the convention featured the strong presence of — and a heavy appeal to — women, Latinos and young people. Speakers evoked their shared values and issued a warning that Republican nominee Mitt Romney would take the country backward.

One speaker after another mocked Romney’s wealth, his past inconsistencies on issues such as abortion, and his party’s dedication to policies that would shrink government and benefit the richest Americans. Romney was ridiculed even in a video paying tribute to the late senator Edward M. Kennedy (D-Mass.), who beat him decisively in a 1994 Senate race.

As the night’s most celebrated speaker, Michelle Obama took aim, obliquely, at Romney’s argument that success in the business world translates into skills for guiding the country through a difficult economic time.

“I’ve seen how the issues that come across a president’s desk are always the hard ones — the problems where no amount of data or numbers will get you to the right answer,” Obama said. “At the end of the day, when it comes time to make that decision, as president, all you have to guide you are your values, and your vision, and the life experiences that make you who you are.”

Julian Castro, the 37-year-old mayor of San Antonio and the convention’s keynote speaker, was more direct in his attack on the Republican nominee: “Mitt Romney, quite simply, doesn’t get it.”

“What we don’t accept is the idea that some folks won’t even get a chance,” Castro said. “And the thing is, Mitt Romney and the Republican Party are perfectly comfortable with that America. In fact, that’s exactly what they’re promising us.”

Some of the harshest criticism of Romney came from past and present Democratic governors, who painted a dire picture of how the nation would look in a Romney presidency.

Maryland’s Martin O’Malley, who is being talked about as a presidential prospect in 2016, warned that Republicans would offer “a country of less.”

“How much less do you really think would be good for our country,” O’Malley asked. “How much less education would be good for our children? How many hungry American kids can we no longer afford to feed? How many fewer college degrees would make us more competitive as a nation?”

The atmosphere was a contrast both from last week’s tightly focused Republican convention in Tampa and from the optimism and idealism of the 2008 Democratic convention.

On the stage in Denver four years ago, Obama introduced her family to a national audience as a quintessential American story, and herself as a devoted sister, daughter, mother and wife.

Her speech Tuesday reprised many of those themes but also updated them, giving a perspective from four years in the White House. Obama, one of the most highly regarded figures in American political life, delivered her speech with an assurance that had delegates cheering and at some points weeping.

“I’ve seen firsthand that being president doesn’t change who you are,” Obama said. “It reveals who you are.”

The Democratic convention began just five days after the Republicans ended theirs. A new Washington Post-ABC News poll suggests that the GOP convention boosted Romney’s standing within his own party — particularly among Republican women, with whom his favorability rose by 20 percentage points — but had a negligible impact with the electorate at large.

The program also featured, as it will throughout the convention, frequent appearances by middle-class Americans from various walks of life. The first lady was introduced by Elaine Brye of Ohio, a mother of five, four of whom are serving in the military.

The convention got underway on a day when the Treasury Department announced a grim milestone: The national debt passed the $16 trillion mark.

House Speaker John A. Boehner (R-Ohio) issued a statement calling it “another sad reminder of President Obama’s broken promise to cut the deficit in half.”

Obama campaign officials, however, said that they will not shy from the deficit issue during the convention — and will use the national spotlight of Obama’s acceptance speech Thursday to make the argument that Republican obstructionism has made the nation’s fiscal situation worse.

The president “has been making these arguments, specifically on deficit reduction, for a couple of years,” Obama deputy campaign manager Stephanie Cutter said at a session with journalists organized by Bloomberg News. “A year ago, he laid out a very specific deficit-reduction plan, which is sitting before Congress. And you can expect him to talk about that, and talk about how we can move that forward.”

At a time when nearly half of all Americans say they are dissatisfied with Obama’s performance as president, the convention also presents an opportunity for Democrats to remind voters of what he has achieved, even at a time of legislative paralysis in Washington.

Former Virginia governor Tim Kaine, who is in a tight race for the Senate, noted that the Obama presidency has seen the end of combat operations in Iraq, a reduction in the number of troops in Afghanistan, the death of Osama bin Laden, the passage of an overhaul of the health-care system, pay-equity legislation for women, and more rights for gay men and lesbians.

“He’s kept his word,” Kaine said. “President Obama is a tough leader who gets results for the American public.”

As his party gathered for their convention here, the president was finishing up a four-day campaign swing through the closely contested states of Iowa, Ohio, Colorado and Virginia.

“Now, the other side may not be eager to talk about their ideas, but on Thursday night I look forward to sharing mine with you,” the president said in Norfolk. “I will offer what I consider a better path forward, a path to create good jobs and strengthen the middle class and grow our economy. The good news, Virginia, is that in just two months you get to choose which path we take.”

Obama’s campaign plans to use the convention itself as an organizing tool, much as it did when the party met in Colorado four years ago. Obama carried North Carolina by less than half a percentage point in 2008 and was the first Democratic candidate for president to win the state since Southerner Jimmy Carter won it in 1976.

David Nakamura and Krissah Thompson contributed to this report.