Members of the Federal Election Commission deadlocked Thursday on whether “super PACs,” which are spending millions of dollars on the 2012 campaigns, can work with candidates on advertisements.

The issue has bedeviled the agency for more than a decade: When can interest groups and politicians work together on political ads without running afoul of restrictions on campaign spending?

The conservative group American Crossroads had asked the commission whether it could produce an ad featuring an incumbent lawmaker talking about issues in the election. The proposed ad would not ask for votes and would appear well before the polls opened.

After a testy meeting lasting more than two hours, the three Democratic commissioners voted to reject the ads planned by Crossroads. None of the Republicans on the six-member commission joined them, leaving the measure short of the four votes needed.

The outcome leaves the matter unsettled, and it is likely to come up again before next year’s elections. For now, though, it is unlikely that lawmakers would expose themselves to possible FEC action by appearing in a super-PAC advertisement.

The Democratic members said they objected to the proposed advertisements because Crossroads stated that its ads were intended to “improve the public’s perception of the featured member of Congress in advance of the 2012 campaign season.” Such a goal means that the ads amount to a “contribution” to the candidate under the law and is therefore prohibited, the Democrats said.

A draft response by Republican commissioners says that the group’s intent is irrelevant, citing a Supreme Court ruling that such subjective judgments could lead to the “bizarre result that identical ads aired at the same time could be protected speech for one speaker, while leading to criminal penalties for another.”

Jonathan Collegio, a spokesman for Crossroads, said that the group’s request follows ads that the Democratic Party ran featuring Sen. Ben Nelson (D-Neb.) talking about his record. Nelson is up for reelection next year, and his seat is likely to be one of a handful that decide whether Democrats keep their majority in the Senate.

Political parties are subject to the same limitations as Crossroads when it comes to coordination with candidates once they have passed a certain limit on spending.

“The FEC today failed to approve actions similar to those taken by Senator Nelson and the Nebraska Democratic Party,” Collegio said. “If Nelson’s coordination was illegal, a vulnerable Democrat would be on a serious hook.”

Neither the Crossroads request nor the proposed FEC responses mention the ads run for Nelson, and Democratic officials say they’ve run similar ads in previous years without incident.

“Crossroads is a shadowy special interest organization that takes unregulated contributions and hides the identity of their contributors,” said Brandon Lorenz, a spokesman for the Nebraska Democratic Party. He said that was “completely different” than his party’s ads.