Democrats know that whatever any additional returns show, they can highlight the details of tax breaks and other accounting maneuvers by the multimillionaire Romney to bolster the perception they seek to exploit that he represents society's fat cats.
Republicans responded by attacking Reid's credibility, and by extension, the president's also.
Reid's tax attack puts GOP in a bind
Romney called on Reid to disclose his source or shut up, insisting he paid lots of taxes in past years, while top party spokesmen and surrogates called Reid a liar and said he was carrying out the attack at the request of the White House.
Obama advisers, benefiting from the continued focus on the matter, denied they were behind Reid's push.
"There is a way to resolve this dispute ... which is for the governor to follow a tradition that was established by his own father many years ago of presidential candidates releasing multiple years of his tax return," White House spokesman Carney chimed in Tuesday.
Carney referred to the decision by George Romney, the former Michigan governor who released 12 years of his tax returns when running for president in 1968. Mitt Romney says he has complied with the law and won't release any further returns that would only get distorted by Democratic attackers.
Earlier Tuesday, a Romney ad on welfare changes by the Obama administration claimed they would "gut welfare reform by dropping work requirements."
"Under Obama's plan, you wouldn't have to work and wouldn't have to train for a job. They just send you your welfare check," the announcer says. "And welfare-to-work goes back to being plain old welfare."
The changes, which would allow states greater flexibility in administering their welfare-to-work programs, were in a directive issued last month by the Department of Health and Human Services.