In response, the Republican National Committee bookmarked Neely's refusal to answer the questions and asked in an email to the press, "How Many Times Will Those Involved in Obama Administration Scandals Refuse to Answer Questions?"
The RNC also noted that executives at the failed energy company Solyndra refused to answer questions at a separate hearing, as did a Justice Department official during a hearing on the Fast and Furious gun operation.
Mike Kelly, a freshman Republican congressman on the committee questioning the GSA, mocked the administration for preaching a "clear and transparent government."
"It is an absolute shame to have to sit here ... and watch as we take the Fifth -- OK, fine, that's your constitutional right -- not sure, cloudy, murky," Kelly said in an angry tirade. "It's pathetic, and I can't tell you how disappointed I am."
On Tuesday, the Democratic National Committee compiled its best stuff into a video, prompting Romney spokeswoman Andrea Saul to respond: "It's ironic that a White House that refuses to talk about Solyndra and pleads the 5th Amendment on President Obama's scandal-plagued GSA would accuse anyone of not being forthcoming."
Congressional Republicans -- and Romney -- have also hounded Obama for telling Russia's president in a much-repeated "hot mic" moment that he would have more "flexibility" after being reelected. The GOP has interpreted that publicly as a warning that Obama could run amok in a second term without worrying about reelection.
Critics and even supporters of the White House say the administration has a way to go before it comes close to matching Obama's 2008 campaign rhetoric, in which he pledged to bring about a new era of government transparency.
They say he can cut back on classifying documents, respond to more requests under the Freedom of Information Act, publicize with whom officials are meeting across all agencies, and shed light on access that lobbyists and campaign donors have in the White House.
A White House spokesman, Eric Schultz, pointed to reports that say the administration has increased the rate in which it acts on FOIA requests, and he noted that a new government website, ethics.gov, lets the public search databases of White House visitors, travel reports, lobbying data and more.
"Over the past three years, Federal agencies have gone to great efforts to make government more transparent and more accessible than ever, to provide people with information that they can use in their daily lives, and to solicit public participation in government decision-making and thus tap the expertise that resides outside of government," Schultz said in a statement.
Transparency advocates say they hope the budding feud between Obama and Romney is sustained so that whoever is president in 2013 can be held to the promises they make on the stump this year.
"We certainly hope that any candidate for the presidency would recognize that in terms of open government, more, not less, will make you more electable and will certainly improve our democracy," said Angela Canterbury, the policy director at the Project on Government Oversight. "Transparency in the candidacy should be an indication of what kind of transparency we might see in an administration."
She added, "In terms of the issue of open government, I think Mitt Romney has a lot of catch-up work to do."