The Barack Obama the nation saw Thursday night is an older, hopefully wiser, and undeniably more realistic version of the candidate who accepted the Democratic nomination in Denver in 2008.

Chastened by four years of partisan infighting in Washington, President Obama replaced the soaring vision he once offered — “hope and change” — with a sobering appraisal that the road to recovery won’t be “quick or easy.”

The second term Mr. Obama wants is certainly within his grasp — as it is for Mr. Romney — but he didn’t clinch the sale. The voters he has to reach, particularly independents who haven’t made up their minds, have yet to be persuaded that his first term was successful, and, second, that he can finish the job if given more time.

On the first part, Mr. Obama has a strong case to make, even though he hasn’t done a good job of it. He pulled the economy out of a steep dive and turned it upward, passed the Affordable Care Act, imposed new limits on Wall Street, killed the world’s No. 1 terrorist, pulled the troops out of Iraq, began the withdrawal from Afghanistan, cut taxes for the middle class, rescued the auto industry and put two moderate female justices on the Supreme Court. He also signed a free trade bill with Colombia and Panama that is particularly important for South Florida.

The second part of the equation is more problematic. His speech contained specific promises that are feasible and desirable. Creating 1 million manufacturing jobs by 2016 would extend the trend of the last few years. The same goes for doubling exports by 2014. Slowing the growth of college tuition in half and training two million workers at community colleges — new proposals — would likewise be welcomed as valuable education initiatives, and probably are doable.

But after that, the picture is murky. Former President Bill Clinton gave Mr. Obama a big assist in his rousing speech to the DNC. Mr. Obama, he said, “inherited a deeply damaged economy, he put a floor under the crash, he began the long, hard road to recovery.” It’s not clear, however, that this laid the foundation for a new economy, as Mr. Clinton suggested.

Exactly how will Mr. Obama do that? He promised to shrink the deficit by $4 trillion, a target the he announced last year, but that’s going to demand shared sacrifice. First, Mr. Obama must make clear what he’s going to demand from the broad middle class in order to get there, and then he has to negotiate successfully with Republicans to get the right balance that can both cut the deficit and boost the economy. Balancing investments with belt-tightening, relief for the middle class with a growing economy — that’s a tall order. We’re waiting to hear specifics about how the president would do it if he wins another term.

Also missing is a bold plan to help states like Florida that remain crippled by the housing crisis. Despite his various initiatives to spark a housing revival, millions are still underwater across the country. It’s time to try something new.

President Obama and Gov. Mitt Romney offer two contrasting visions for America. The diversity of people and faces to be found in the delegates at the convention in Charlotte suggest that Mr. Obama’s version holds greater promise for the kind of country that America is becoming, one that reflects today’s South Florida.

In his first term, however, he failed to translate necessary pieces of his legislative program into reality. Persuading voters that he can do it in a second term remains his biggest electoral challenge.