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.
Barack Obama has used the annual White House correspondents' dinner to crack jokes about his healthcare policy, his political opponents and Vladimir Putin.