WASHINGTON — A counterattacking Mitt Romney is seeking to shift political attention away from his business tenure and his tax returns with a fresh assault on President Barack Obama’s record. Obama, anxious about losing a financial edge in the contest, is turning to Republican-tilted Texas to raise money from gay, Latino and big-dollar donors.

Romney planned to campaign in the Pittsburgh area today, stepping up his criticism of Obama in a state that has proven to be a tough presidential battleground for the Republican Party. Romney is accusing Obama of engaging in cronyism, citing federal grants and loan guarantees to alternative energy companies run by Obama backers and donors.

Obama is expected to sustain his offensive against Romney, claiming the Republican’s tax policies would benefit the rich and cost jobs. His re-election campaign continued to draw attention to Romney’s time at Bain Capital, the private equity firm he founded in 1984. But Obama’s central goal in Texas was to draw in money; he was holding two fundraisers in Austin and two in San Antonio, with an estimated haul of at least $5 million.

The events came as a top Romney aide floated the possibility Monday that he may name his vice presidential selection by week’s end, raising the level of intrigue around what may be Romney’s most significant decision before Election Day. But the timing was not certain. Romney senior advisor Eric Fehrnstrom initially said that while Romney had not yet made his pick, the selection could be announced in the coming days. He later downplayed the remark, suggesting the decision could come any time between now and the Republican National Convention at the end of August.

In choosing Texas to raise money, Obama was traveling to a state that has not voted Democratic in a presidential contest since 1976. But Texas ranks among the states with the largest concentrations of wealth, along with New York, California, Florida and Illinois. Republicans typically raise more in Texas than Democrats. So far this election, Obama has raised $4.5 million from the state and the Democratic National Committee has raised $1.7 million, compared with $7.1 million for Romney and $5.3 million for the Republican Party.

Obama is holding one event in San Antonio aimed in part at Latinos, featuring actress Eva Longoria. Another event in Austin is co-sponsored by the Democratic National Committee’s LGBT Council. He also is holding two smaller events with high-dollar donors.

Campaigning in Ohio on Monday, 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 cited campaign disclosure reports showing that the author of that article, Reed College economist Kimberly A. Clausing, has donated money to Obama’s campaign.

How to tax the foreign earnings of companies is a hotly debated topic. Corporate executives, including some who serve on Obama advisory boards, argue that taxing those profits hurts job creation by discouraging companies from reinvesting that money in the U.S.

The Obama camp was also airing an ad in the Pittsburgh media market today taking issue with Romney’s decision to only release two years of his personal tax returns. The ad questions whether Romney has avoided paying his share of taxes in certain years.

Romney has released his 2010 tax return, which showed he paid an effective rate of about 15 percent on his taxes, and has said he will release his 2011 return. He has said he will not release other returns. The ad was only running for one day, a sign it was meant to drive media coverage rather than draw the attention of television viewers.

In its counteroffensive, the Romney camp contended that Obama’s Energy Department has steered loans and grants to several companies connected to the president’s political supporters.

“This is a time when it’s good to be a friend of the Obama campaign, because you might be able to get some money for your business. But it’s not so good to be middle class in America,” Romney told donors in Jackson, Miss., where he raised more than $1.7 million Monday evening following a Baton Rouge, La., luncheon that netted $2 million.

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.”