Sure enough, the Democratic incumbent showed no sign of letting up.
Rallying for support in crucial Ohio, Obama said Romney's proposal to free companies from taxes on their foreign holdings would displace American workers. The president cited a study he said concluded that "Gov. Romney's economic plan would in fact create 800,000 jobs. There's only one problem, the jobs wouldn't be in America."
Romney's campaign, itself moving to the attack, contended that Obama's Energy Department has steered loans and grants to several companies connected to the president's political supporters.
Romney, speaking to donors in Baton Rouge, La., said Obama had a policy of "taking your tax dollars and putting it in businesses owned by contributors to his campaign. And that is smelly at best. It stinks."
Romney aides cited well-known cases, such as Solyndra, a California solar energy company that went bankrupt, and some less-publicized cases. They include Westly Group, a venture capital firm whose affiliated companies have received federal loans and grants.
Steve Westly, the company's founder, is a major Obama campaign fund-raiser.
Obama campaign spokeswoman Jen Psaki said the Energy Department's decisions "were made without regard to political connections." She said some grants have gone to projects with "just as robust connections to Republican campaigns and donors."
While Obama held a freewheeling town hall in Ohio, Romney raised money in the safely GOP states of Louisiana and Mississippi.
He told donors who paid as much as $50,000 to attend a Jackson, Miss., fund-raiser that it was a good time to be a friend of the Obama campaign, but not a good time to be in the middle class.
"I know that people in this room are probably doing relatively well, relative to folks across this country. But not everyone in America is doing so well right now," he said. "The waiters and waitresses that come in and out of this room and offer us refreshments - they're not having a good year."
Romney, who struggled during the GOP primary to explain his suggestion that he doesn't care about the nation's very poor, spoke directly to the poor Monday.
"We're the party of people who want to get rich," he said. "And we're also the party of people who want to care to help people from getting poor. We want to help the poor."
Addressing another major election point of interest, top Romney adviser Eric Fehrnstrom told the Associated Press that the campaign may announce a vice presidential choice by the end of the week. That would be sooner than many expected, and some Democrats suggested it was an effort to turn attention from Bain.
The last several days of the campaign have centered on Romney's work at Bain Capital and whether he has been straightforward about the timing of his departure, a line of attack that Obama is exploiting to try to undermine public support in Romney's business credentials and trustworthiness.
Obama assailed Romney's tax plans for U.S. businesses on Monday. At his Ohio event, Obama cited an article in the publication Tax Notes suggesting Romney's tax proposals would encourage U.S. companies to create up to 800,000 jobs overseas. Romney supports "a territorial tax system," which would allow overseas profits made by U.S. companies to avoid federal taxation.
Romney's campaign cited campaign disclosure reports showing that the article's author, Reed College economist Kimberly A. Clausing, has donated money to Obama's campaign. Republicans say Romney's overall tax proposals would encourage greater job growth at home.
For all the tax talk, the presidential campaign couldn't seem to shake Bain, the company that Romney led in the 1990s to numerous successful corporate restructurings, and to some less happy ventures that ended in bankruptcy or other problems.
Romney traveled to Louisiana to attend a private fundraiser alongside Gov. Bobby Jindal, who is among those on Romney's short list for vice president.