Reclaiming the governor's mansions in New Jersey and Virginia demonstrated the Republican Party "moved beyond our past losses and no message," Steele told CNN Wednesday.
In New Jersey, Gov. Jon Corzine conceded the election to former U.S. Attorney Chris Christie, who picked up about half the vote to 45 percent for Corzine and 5 percent for Chris Daggett, a former Republican running as an independent.
In Virginia, former Republican state Attorney General Robert McDonnell won a decisive victory over state Sen. Creigh Deeds.
Independent voters, critical to Barack Obama's 2008 presidential win, flocked to GOP gubernatorial candidates because "issues that mattered (to them) were not being addressed or being addressed in a way that they didn't appreciate," Steele said.
Democratic National Committee Chairman Tim Kaine, outgoing Virginia governor, downplayed the GOP wins, saying exit polls indicated people "voted based on local issues," and didn't reflect a backlash against Obama.
The president remains popular in New Jersey and Virginia, Kaine said, noting historically in his state the party in the White House lost the governorship in the odd-year election.
The loss of independent support "is something we're going to have to look at," Kaine told CNN.
A Democratic win in upstate New York's 23rd congressional district, despite being "great Shakespearean theater," only showed "you've got to have a primary process," Steele said.
Democrat Bill Owens won a special election in the heavily Republican district. Doug Hoffman, running as a third-party GOP conservative, forced Republican candidate Dede Scozzafava out of the race with help from nationally known conservative figures. Local Republican leaders selected Scozzafava for the ballot.
Kaine said the intraparty squabbling in New York is a continuation of the GOP "marginalizing itself by saying moderates aren't welcome" that likely will have "some significance" in the 2010 midterms.
Steele looked at Tuesday's results cautiously, saying, "I'm not so quick to say this portends great things for Republican Party. We have a lot of work to do. Last night was an example (of what happens) when elected officials don't listen to what the people are saying."