Updated

The White House suggested Wednesday that the $10 million spent by unions in the Arkansas Democratic Senate primary runoff "might have come in more handy" in high-stakes general elections this November -- drawing fierce criticism from labor leaders who insist their money was well-spent.

Just hours after Sen. Blanche Lincoln beat labor-backed candidate Lt. Gov. Bill Halter in Tuesday's runoff, an unnamed White House official told Politico newspaper that "organized labor just flushed $10 million of their members' money down the toilet on a pointless exercise."

Asked about the official's remark, White House Press Secretary Robert Gibbs said President Obama doesn't "necessarily agree with that characterization" but "I think that whether or not that money might have been better spent in the fall on closer elections between somebody -- between people who cared about an agenda that benefited working families and those that didn't -- that money might have come in more handy then."

Lincoln, a centrist Democrat and two-term incumbent, narrowly beat the left-leaning Halter on Tuesday, 52 to 48 percent.

Labor unions poured millions into Halter's candidacy after Lincoln did not support a bill making it easier to form unions. They also criticized the two-term Democrat and chairwoman of the Senate Agriculture Committee for "flip-flopping" on the health care overhaul legislation. Lincoln voted for the bill.

On Wednesday, the AFL-CIO justified the millions spent in a high-stakes gambit that failed.

AFL-CIO Deputy Chief of Staff Thea Lee insisted that forcing Lincoln into a runoff and coming within a few thousand votes of unseating her had achieved the union's goal -- getting other wayward Democrats to think twice before crossing labor.

"It was a good race and we're not sorry we fought it," Lee told Fox News on Wednesday. "(Unions) wanted to send a strong message -- not just to Blanche Lincoln -- but also to Democrats around the country that working families expect our members of Congress to stand with us on issues that matter, whether it's labor law reform, trade, health care, work place safety.

"People shouldn't take the support of unions for granted," added Lee. "They shouldn't assume that because they have a Democrat next to their name that unions will automatically support them. They need to earn that support."