CAPITOL — Gov. Eliot Spitzer got little political support Tuesday as speculation continued about his possible resignation after being caught in a prostitution scandal.

Spitzer’s fellow Democrat, 20th District U.S. Rep. Kirsten Gillibrand, went further than most area Democrats, issuing a statement that said: “If these serious allegations are true, the governor will have no choice but to resign.”

Assembly Minority Leader James Tedisco, R-Schenectady, went further still, calling for Spitzer’s impeachment if he does not exit voluntarily by Thursday.

Tedisco said he believes Spitzer “is negotiating with law enforcement officers” about criminal charges he may be facing and he is willing to give him some time to do that. But if the resignation has not happened by Thursday afternoon, Tedisco said, then he will introduce a resolution of impeachment that the Assembly minority counsel’s office is preparing.

“It’s not something we relish doing,” Tedisco said, noting it has been almost a century since a governor was impeached. But the state is gridlocked and needs to move on from Spitzer, he said.

If the Democrat-controlled Assembly were to vote in the majority to impeach, a trial would be held before the Senate, with members of the Court of Appeals also participating.

Schenectady County Republican Chairman Thomas Buchanan issued a statement denouncing local Democrats for their ties to Spitzer, focusing on county Legislature Chairwoman Susan Savage of Niskayuna.

Buchanan cited campaign contributions made by Savage to Spitzer “and receipt of a lucrative six-figure job from him,” saying she “should renounce any support that she has given him and should demand that he resign immediately.”

Buchanan was referring to a $100,000-per-year job Savage started this year at the state Office of Real Property Services.

In response, Savage put out a statement about Spitzer saying: “I am stunned and disappointed as are all residents of New York state. My heart goes out to Governor Spitzer’s family.”

Another Democrat, Assemblyman Jack McEneny of Albany, said: “When you lose the moral high ground, when you can’t do the job, it’s time to do the right thing, and do it quickly.”

While his comments clearly implied that the governor should resign, McEneny said he was “avoiding the ‘R’ word.”

Senate Republicans were keeping a lower profile. Scott Reif, spokesman for Senate Majority Leader Joseph Bruno, R-Brunswick, when asked about impeachment, would say only: “We are focused on moving forward and doing the budget.”

Assembly Speaker Sheldon Silver, D-Manhattan, declined to answer directly when asked if Spitzer should resign.

“He has to evaluate the situation and do what’s best for him,” he said.

About an hour later, Silver said “The facts are still being uncovered” regarding Spitzer’s situation, and “I think the governor has to make the determination” about whether or not he should resign.

Silver said the Assembly still plans to pass its one-house budget today, and he expects the Senate will act, too. Then, Silver said, they would proceed to conference committees — indicating that legislative action on the budget can proceed despite the turmoil in the executive branch.

Reif confirmed that the Senate plan remains to pass the budget today, and then go to conference committees with the Assembly.

Assembly Majority Leader Ron Canestrari, D-Cohoes, said the scandal was “not a pretty picture,” but “we have to let it play out.” He said he was not going to speculate or say what the governor should do.

Another senior Assembly Democrat, Richard Brodsky of Westchester County, said “The governor has an obligation to come back to us as he said he would,” and that the situation “ought to be resolved quickly.” But he also said the presumption of innocence applies, and declined to say whether the governor should resign.

Terry O’Neill, an Albany activist on law enforcement issues, said Spitzer would be “ineffectual until proven not guilty.”

Cardinal Edward Egan, archbishop of New York, was another who declined to say whether Spitzer should resign. “I’m going to withhold my judgment but not withhold my prayers,” said Egan, who was at the Capitol to lobby legislative leaders about other issues.

Russ Haven, legislative director for the New York Public Interest Research Group, said Spitzer might try to hold on. “Everyone is living moment by moment and rumor by rumor,” he said.

State troopers have been more visible than usual at the Capitol since the scandal broke, and they were stationed outside Lt. Gov. David Paterson’s offices on the second and third floors.

“There’s nothing going on,” said Spitzer spokeswoman Jennifer Givner Tuesday evening.

A senior legislative staffer said he had heard that the staffs of Spitzer and Paterson were holding transition talks. However, in remarks quoted on The New York Times’ Web site Tuesday afternoon, Paterson said he had not been in transition discussions or spoken that day to Spitzer. The governor remained in New York City, and his schedule for today said he would be staying there.