(CNN) -- Wisconsin Democrats' failed effort to seize control of the state Senate in Tuesday's special elections left some Republican groups cheering, but analysts in the state cautioned against seeing the results as a national rallying point for the GOP.
"Yesterday overall was probably a political draw," said Mordecai Lee, a political science professor with the University of Wisconsin- Milwaukee.
Republicans held onto four of six state Senate seats in jeopardy Tuesday, according to Wisconsin news media. The state said official results will begin to arrive Thursday.
"Wisconsin voters rejected the reckless spending of Wisconsin Democrats and the downgrade-inducing policies of their Washington counterparts," Republican National Committee Chairman Reince Priebus said in a statement hailing the results. And Tea Party Express chief strategist Sal Russo added, "Wisconsin has set an example that the nation as a whole should follow."
Wisconsin's Democratic Party, meanwhile, said the elections "showed just how vulnerable Republicans are in the November 2012 elections -- and how vulnerable Gov. (Scott) Walker is to a recall election himself." There was "significant Republican advantage" in the recalls, the party said.
Democrats had hoped to build momentum to oust Walker, who was elected in November and can't be recalled until after he serves a year in office.
The recall elections, sparked by a battle over union power and Walker's controversial legislation earlier this year restricting collective bargaining, ended up focusing mostly on broad economic issues, said Charles Franklin, political science professor with the University of Wisconsin-Madison.
"The Democrats, the unions, failed to send the message they wanted to send," he said. "Is this an absolute ratification of Republican policies? No, I don't think so.
"It shows that this is an issue that Republicans may prevail on, but they prevail only after a tremendous fight and tremendous expense," he added.
Money from outside groups flowed into the state to fund the recall battles, leading to a slew of television ads in the districts.
A Democratic incumbent state senator held onto his seat in a previous recall election in July, and two other Democrats will be on the ballot Tuesday.
And Franklin said there was another important lesson for the country in Tuesday's elections: The turnout was "stunning." The union battle that drew national headlines invigorated voters, he said.
"This is political dynamite," Franklin said. "We had unbelievable turnout rates yesterday. Most of the districts exceeded the Supreme Court race from April, which itself blew past all previous records."
The Milwaukee Journal Sentinel's "The Wisconsin Voter" blog reported that 44% of voting-age adults in the districts turned out in the districts where recall votes were held, approaching the 49% combined turnout rate in those districts in last year's race for governor.
"You want polarized politics, high engagement, massive turnout and very expensive elections? We have the recipe for it," Franklin said.
Lee said the results of the elections showed that swing voters are a dying breed.
"The national implications are that the voters are increasingly close-minded about their party preferences" and not influenced by developments in the news, he said.
Polls for several months have shown the electorate "remarkably unchanging," Lee said.
"It's becoming a battle of the bases. It's almost like there are not authentic swing voters anymore. They've almost disappeared."
The two districts in which Democrats won generally lean Democratic, he said, so the Democratic victories came as little surprise.
Lee said the results suggest the 2012 presidential election will operate similarly, with entrenched voters maintaining their commitment to parties, and the race boiling down to much more a battle of turnout than a battle for swing voters.
But Tom Holbrook, also a political science professor with the University of Wisconsin-Milwaukee, said the election doesn't offer any new insight on the state of U.S. politics. "Trying to read anything into 2012 from this probably means people have too much time on their hands," he said.
Holbrook added, "I guess the real implication would be that politics are pretty predictable."
Walker set off a firestorm in January when he moved to curtail the collective bargaining rights of most state employees. With majorities in both houses of the Legislature, Walker and his GOP allies voted to limit raises for public employees except police and firefighters to the rate of inflation, bar unions from deducting dues from workers' paychecks and force them to hold a new certification vote every year.
Republicans insisted it was necessary to control the skyrocketing costs of public employee benefits and close the budget shortfall. Democrats argued it was an attempt to gut public-sector labor unions, one of their core constituencies.
The state Supreme Court upheld the law in June.
In a statement Tuesday night, Walker praised his economic record and said he had reached out to leaders of both parties in the state legislature. "In the days ahead I look forward to working with legislators of both parties to grow jobs for Wisconsin and move our state forward," he said.
CNN's Gabriella Schwarz contributed to this report.