His declaration, in an interview with NBC, came as a new poll showed his approval ratings moving past 50% for the first time since May 2011.
The ABC News/Washington Post survey also suggests Mr Obama would beat Republican front-runner Mitt Romney.
Mr Romney and his rivals are now campaigning in Colorado and Minnesota after his weekend caucus win in Nevada.
States across the US are currently holding nominating contests to pick a Republican nominee to challenge Mr Obama in November’s general election.
Mr Obama’s NBC interview was broadcast ahead of the Super Bowl, the most-watched TV event of the year.
It came two days after improved employment figures prompted analysts to suggest his prospects for securing four more years in the White House were improving.
“I deserve a second term, but I am not done,” Mr Obama said. “We’ve created 3.7 million jobs in the last 23 months.
“We’ve created the most jobs since 2005, the most manufacturing jobs since 1990, but we’re not finished.
“What I’m going to just keep on doing is plodding away, very persistent. And you know what? One of the things about being president is you get better as time goes on.”
The ABC News/Washington Post poll – carried out over the end of last week and into the weekend – indicated that some of the positive economic data of the past few months could be filtering through to the electorate.
Asked directly to choose a president if an election were being held now, 51% of the 1,000 respondents chose Mr Obama, with Mr Romney on 45%.
Matched against former House of Representatives Speaker Newt Gingrich, who is running second in the Republican race, Mr Obama came out ahead by a wider margin, 54% to 43%.
Mitt Romney is campaigning in Colorado on the eve of the caucuses there
Mr Gingrich, as well as Ron Paul and Rick Santorum, has vowed to stay in the nomination fight, despite seeing Mr Romney win 50% of the votes in the Nevada Republican caucuses at the weekend.
Although his approval ratings are up, Mr Obama remains a polarising figure. Asked whether or not he should have a second term in office – but without being asked to choose between him and an alternative president – the respondents were split 49%-49%.
Despite his winning record in primary season, Mr Romney has endured a barrage of hostile advertisements from rivals, and a lengthy focus on his wealth and business interests.
Some 52% of those polled said the more they learn about the former Massachusetts governor, the less they like him.
However, Mr Romney is still considered the favoured Republican candidate on economic issues, the poll suggests.
Although he is the front-runner, Mr Romney faces a long path to the Republican nomination.
He needs 1,144 delegates from across the 50 states to secure the mantle, and currently has 101 to his name. Mr Gingrich is his nearest challenger, with 32, while Mr Paul has 17 and Mr Santorum is on nine.
On Monday, the Romney campaign turned its attacks on Mr Santorum, after recent polling showed the former Pennsylvania senator ahead of Mr Romney in Minnesota and second in Colorado.
Tim Pawlenty, a former Republican presidential candidate and Romney supporter, told reporters that Mr Santorum has “held himself out as the perfect or near perfect conservative when in fact, that’s not his record”.
“As a US senator, he was a leading earmarker and pork-barrel spender,” Mr Pawlenty said, referring to ways lawmakers steer federal dollars towards their home districts.
The Colorado and Minnesota caucuses will be held 7 February 2012.