ALBANY – Democrats, riding the coattails of President Obama’s comfortable victory among New York voters as they did four years ago, appear in preliminary results to have retaken control of the State Senate.

But, Albany being Albany, it doesn’t mean Democrats will actually run the 63-member chamber come January, even if the 33 seats they tentatively claimed Tuesday hold in the final tally.

The Capitol, long known for its dysfunction, now find itself entering another one of its uncertain phases – which could last weeks or months – as election lawyers will now begin the work of challenging paper ballots in two still-uncertain races in the Hudson Valley. And, as significantly, discussions were already under way by Senate Republicans on how to maintain some semblance of power by recruiting four renegade Democratic lawmakers who two years ago broke to form their own independent caucus.

“If it becomes a mathematical impossibility for there to be more Republicans in raw numbers than Democrats, then I think a coalition is in the Senate’s and the state’s best interest,” said Sen. Patrick M. Gallivan, R-Elma, who handily won re-election Tuesday.

Democrats dismissed the GOP claims as fading bluster and said that in the end, they will be able to make deals with the four breakaway Senate Democrats – despite harsh verbal attacks they leveled against them in the last two years – to get them to rejoin their ranks to take Senate control.

“Sure, we’d gladly welcome them back,” said Sen. Michael N. Gianaris, D-Queens, who heads the Senate Democratic Campaign Committee.

Overnight in Albany, Gov. Andrew M. Cuomo’s much-touted description of the Capitol as the home of a new breed of cooperation, and results, has become murky and potentially bumpy – a potential thorn for a governor eyeing a possible White House run in four years.

Uncertain is what the four breakaway Democrats of the Independent Democratic Caucus will do. The group’s leader, Sen. Jeffrey D. Klein, D-Bronx, wasn’t doing interviews Wednesday, and the group put out a brief statement saying New York needs a “strong, stable government.”

Unofficial results show, for now, Democrats with 33 seats in what will be a 63-member Senate in January; it will take 32 votes to pass a bill.

Wednesday, Democrats were gleeful about the Senate results. They were badly outspent by Senate Republicans and had no real campaign help from Cuomo. Since taking office two years ago, Cuomo regularly has praised the GOP-controlled Senate for working with him on key fiscal and policy areas.

Republicans, meanwhile, were conceding nothing. Lawyers on both sides prepared to recount machine votes from Tuesday, as well as – in the case of a contested seat in the Hudson Valley that a Democratic newcomer is leading by only 139 votes – counting nearly 8,000 paper ballots that can’t even be opened for two weeks as a result of later deadlines for receipt of absentee ballots because of Superstorm Sandy.

That district, stretching from Montgomery County all the way down to Ulster County, was created this year by Senate Republicans as a new 63rd seat, specifically to give the GOP an edge in the elections over the present 62-member chamber.

For the governor, a takeover by more-left-leaning Democrats would present a major challenge to his ability to maintain the fiscally moderate stance he enjoyed with Republicans.

Cuomo, who endorsed Republican Sen. Steve Saland, a Poughkeepsie Republican trailing in unofficial results, has been criticized by some Democrats for abandoning his party to help Republicans. They point as chief evidence to his willingness to break his 2010 campaign pledge to veto any legislative lines drawn during this year’s redistricting process, which was controlled by Republicans in the Senate, unless done so by an independent panel.

If Saland does lose – he was trailing his Democratic opponent by 1,600 votes Wednesday – it would mean three of four Senate Republicans who broke party ranks last year to support Cuomo’s legislation to legalize same-sex marriage will not return to Albany in January. The only one who will: Sen. Mark J. Grisanti of Buffalo, who handily won Tuesday. Less than a year ago, Grisanti was considered by many at the Capitol as the Senate’s most vulnerable Republican.

One Senate Democrat who opposed the gay marriage law, Ruben Diaz Sr. of the Bronx, called Saland’s showing “an embarrassing defeat” for Cuomo.

Cuomo’s office declined to comment on the Senate elections.

Besides the two Hudson Valley seats still in play, Republicans say a Queens seat – in a district especially hammered in last week’s storm – could still swing their way, even though the GOP candidate conceded defeat.

Senate Deputy Majority Leader Thomas W. Libous, R-Binghamton, said he believes that the GOP “will have a hand” in controlling the Senate come January.

Will that mean help from Democrats? “It might. It might not. It could very well mean there will be a very strong coalition working relationship with members of the other side of the aisle,” Libous said. “I don’t think there’s anything wrong with that. That could be historic and very positive.”

Libous said that there are no assurances from any Democrats, and no negotiations yet under way, about forming a coalition.

Democrats insist that, in the end, the four breakaway Democrats will want to be in a majority that represents their districts that are dominated by Democratic voters.

“In an unprecedented fashion, voters in this state delivered a mandate that they want a Democratic Senate to advance a progressive agenda in this state, and I would hope that anyone elected [Tuesday] night as a Democrat would pay attention to that clear choice of the people they represent,” Gianaris said.

Democrats said the Republicans got what they deserved for pushing through what they called a gerrymandered set of Senate district boundaries this year after promising reform groups to leave the process to an independent panel.

“The chicanery of the Republicans going back on their word to do independent redistricting blew up in their face,” said Sen. Timothy M. Kennedy, D-Buffalo.

Kennedy dismissed GOP claims that a Democratic-run Senate will ignore many upstate issues, as was often the case when the party ran the chamber in 2009 and 2010.

“The Republicans have done a masterful job at the politics of demonizing the Democratic conference,” Kennedy said.

Noting that the Democrats picked up a Rochester seat now held by a Republican, Kennedy said that upstate will not be ignored. “Upstate will absolutely have a strong voice, if not a stronger voice, than they’ve ever had in the New York State Senate.”

But Gallivan said that if the Republicans don’t have the numbers after all the votes are counted, deals should be made.

“If there needs to be some sort of coalition to make sure there remains a balance in the Senate, so be it,” he said. “We’ll have to do the best we can to work together.”