On the heels of Wisconsin Gov. Scott Walker's history-making recall victory, the governor of nearby Indiana with his own record of curtailing union benefits suggested public-sector unions are past their prime and should be abolished.

"I think, really, government works better without them," Indiana Gov. Mitch Daniels told "Fox News Sunday," when asked whether public-worker unions should even exist.

Daniels had cracked down on collective bargaining for state workers as soon as he took office in 2005, six years before Walker and his GOP allies in the state legislature started down the same path -- triggering a backlash that forced him to stand for election this past Tuesday. Walker made history as the first governor to survive the recall test, beating Democrat Tom Barrett.

Daniels said that vote should send a message about the problems with public-sector unions.

"I think the message is that, first of all, voters are seeing the fundamental unfairness of government becoming its own special interest group, sitting on both sides of the table," he said.

The pushback on union benefits extends far beyond Wisconsin. In California, voters in San Diego and San Jose just backed ballot measures to curtail retirement benefits for city workers. Speaking on CBS' "Face the Nation," Walker said he thinks his victory is a sign that Americans want "people willing to take on the tough issues" in his state and "across the country."

Daniels said private-sector unions, while in decline in America, remain "necessary." But he suggested the public-sector unions have hobbled governments by gobbling up taxpayer resources with generous benefits and salaries and "bulletproof" job protections.

Daniels said he hopes Tuesday's election marks "some kind of turning point" in addressing the public union system.

Top representatives of that system, though, pushed back on the idea that the Wisconsin election opens the door to a dismantling of public-union benefits.

Dennis Van Roekel, president of the National Education Association, said Walker's victory was in part a product of "unlimited corporate funding in elections." He said Walker's side simply was able to push out its message better than the governor's opponents.

AFL-CIO Deputy Chief of Staff Thea Lee said the public does support pensions for public- and private-sector workers.

"That's something that people do support at the end of the day. We have to figure out how to fund it, we have to figure out how to make it viable, but I don't think that voters in this country want to go to a place where our elderly people are living in poverty," she said. "When times are tough, people are trying to figure out who's to blame, but we need to be able to fund our public sector."

Public-sector workers continue to enjoy better benefits than in the private sector. About 64 percent of private-sector workers have access to pensions, compared with 90 percent of state and local government workers. Private-sector workers earn an average of $8.53 in benefits per hour, while government workers earn $14.31 in benefits per hour.

Lee, though, said government workers are not overpaid when salaries are taken into consideration, noting that highly skilled professionals like doctors make less in the public than private sectors.

She said the debate should focus on how the private sector can offer better retirement benefits, not on how the public sector can offer fewer benefits.