But these initial skirmishes, which will continue through the spring and early summer, are not expected to morph into a full-blown general-election campaign yet, say political analysts.
Mr. Romney has spent almost $14 million on TV advertising, while Mr. Obama, who has had no primary challenger, has spent only $2.2 million, according to Kantar Media.
Super PACs supporting Mr. Romney have spent more than $50 million on advertising and those supporting Mr. Obama only about $6 million.
"Romney has already begun to pivot toward Obama, but he can't do so fully until [former Pennsylvania Sen. Rick] Santorum suspends his campaign or scales back," said University of Virginia political-science professor Larry Sabato. "There has been a near consensus that the GOP race is over, and we're onto a Romney-Obama fight. There's just one problem: No one told Rick Santorum."
The president attacked Mr. Romney by name for the first time this week, and ran his first ad blasting the Republican in key swing states. The president's campaign also has jumped on media reports that Mr. Romney took advantage of a loophole in federal ethics laws to avoid disclosing the extent and nature of his financial holdings.
Meanwhile, bolstered by primary wins in Wisconsin, Maryland and Washington, D.C., Mr. Romney used the platform provided by the Associated Press' annual convention to attack President Obama for running a "hide and seek" campaign. He also ripped the president for telling the Russian president, in comments captured by a still-live microphone, that he could be more flexible after November's elections.
Having more than half the 1,144 delegates needed to win the GOP nomination, Mr. Romney hopes Mr. Santorum will make his last stand on April 24 when Pennsylvania holds its primary. An embarrassing defeat may be in the works for the former Pennsylvania senator as his poll numbers are falling in his home state while Mr. Romney's are on the rise.
"Romney wants to treat Santorum as the walking dead," said Norman Ornstein, a resident scholar at the American Enterprise Institute. "He desperately wants to turn his entire focus on Obama and shake that Etch a Sketch."
A top Romney campaign aide said strategy would change when it came time to battle Obama, "like shaking up an Etch a Sketch," a child's drawing tablet in which nothing is ever permanent. The comment opened the Romney campaign to attacks regarding his many position changes.
If he survives the Pennsylvania primary, Mr. Santorum may decide to campaign through May, when several states with evangelical voters, including Texas, North Carolina and Arkansas, hold their primaries.
"We may be still a step or two away from the general-election mode," Mr. Sabato said.
Some of Mr. Obama's money was spent on a 30-second ad titled "Remember" that 's running in the key swing states of Colorado, Florida, Iowa, Nevada, Ohio and Virginia. It calls Mr. Romney an ally of oil companies.
A second ad from Priorities USA -- a super PAC supporting Mr. Obama -- released this week damns Mr. Romney for his connection to oil companies. The ad is running on TV and online in the same states as "Remember," as well as in Michigan and New Mexico, two other swing states.
Mr. Romney has struck back with ads on his YouTube Channel.
Mr. Ornstein said Mr. Romney can't afford to spend much money on TV ads targeting Obama until he "gets rid of the gnat that 's buzzing around him."
"Right now both campaigns are going to start doing things designed to get news attention and use YouTube more," he said.