Obama and his campaign strategists have targeted the Republican front-runner almost exclusively in recent days, the Washington publication says.
After Romney dismissed the economic impact of the president's proposed extension of the payroll tax holiday, Obama sent a web video to supporters.
"One of the leading Republican presidential candidates suggested we .... allow taxes to rise by up to $1,000 next year for struggling middle-class families," Obama said. "That's not how you build an economy where middle-class families can get ahead. That's not how we put people back to work. We don't have to accept that future. I certainly don't."
Leading Democrats told Politico they were angry other GOP candidates had not gone after Romney more aggressively for shifts in his stances on abortion rights, civil unions and healthcare reform.
"The other Republicans have sucked so bad we didn't have any choice" but to target Romney, an Obama ally who spoke on condition of anonymity told Politico.
David Axelrod, a senior Obama strategist, took aim at Romney this week, calling him an insincere hypocrite after a Romney spokesman likened Obama to former President Herbert Hoover and said the president had turned the country into an "economic disaster zone."
In an e-mail message to Politico, Axelrod retorted: "It's ironic that a candidate who's advocating the deregulation of Wall Street, massive new tax cuts for corporations and the wealthy and trade wars as a means of lifting our economy would liken others to Herbert Hoover. Allowing that he can always change his positions, and often does, Romney's policies today are exactly the ones that led us into a disaster in the 1920s and again in the 2000s. He's carrying Hoover's tattered banner."