The healthcare policy has serious IT issues, prompting the joke: "In 2008 my slogan was: 'Yes we can.' In 2013 my slogan was: 'Control-alt-delete.'"
And he ridiculed media commentators for their apparent obsession with Mr Putin's bare chest.
Dozens of celebrities, journalists and politicians were at the dinner.
The roll-out of healthcare.gov, Mr Obama's main policy initiative of his second term, provided much of the humour.
The president made several references to computer malfunctions.
"Does anybody know how to fix this," he asked, pretending that the overhead projector had failed to work.
Health Secretary Kathleen Sebelius, who quit as a result of the IT issues, stepped up and said: "I got this. I see it all the time."
The president used Mr Putin as a way of lampooning some conservative commentators and political opponents.
"Last year [conservative commentator] Pat Buchanan said Putin is headed straight for the Nobel Peace Prize... to be fair they give those to just about anybody these days. So it could happen," he said. Mr Obama was given the award in 2009 having been nominated for it after less than two weeks in office.
"[Republican] Mike Huckabee and [conservative commentator] Sean Hannity keep talking about his bare chest, which is kind of weird."
The charity event is traditionally used by presidents to ridicule their opponents, but also laugh at themselves.

Stephen Downing, 55, was jailed for five years after he and his partner Claire Holmes, 26, both of Marsh Green, earlier pleading guilty to supplying the class A drug
Downing also admitted mortgage fraud and six counts of money laundering.
Holmes, 26, was jailed for two years and six months.
Downing, who owned seven houses, a strip of land and business premises in Wigan, has been ordered to pay back nearly Â£400,000 and Holmes more than Â£5,000.
Police searched their home in October 2012 and found cocaine and drug-dealing paraphernalia and large amounts of cash.
Officers returned in 2013 and found more cocaine, about Â£45,000 in cash, debt lists and details of drug deals.
In 2005 Downing had illegally remortgaged his home and used the money to purchase other properties, the police investigation also revealed.
The pair tried to blame the drug dealing on Downing's son and he was charged as a result of this false testimony, Greater Manchester Police said.
He was acquitted in January when they changed their pleas.
Constable Peter Jackson from Greater Manchester Police said the pair were "reprehensible".
"Downing and Holmes were determined to live a lifestyle funded entirely by nefarious means. They made their money by dealing drugs and Downing then tried to hide this by fraudulently purchasing and leasing out a string of properties which supplied him with rental income."
He said when they blamed Downing's son. it was a "a perfect of example of the phrase 'no honour amongst thieves'"
Barack Obama has used the annual White House correspondents' dinner to crack jokes about his healthcare policy, his political opponents and Vladimir Putin.
[NEXT_CONCEPT]
A couple have been jailed for dealing cocaine from their home in Wigan and ordered to pay back the money they made illegally.