After 17 months of delay and four secret hearings, Senate Democrats are concerned that new obstacles may prevent a vote on the nomination of CIA general counsel Stanley Sporkin to the U.S. District Court here before Congress adjourns.

Recent agreement by the Senate Judiciary Committee to vote on Sporkin by next week may be unraveling because of new procedural delays, congressional staff members said. Further delay would kill the nomination for this session of Congress and require that President Reagan submit it next year for a third time.

Sen. Jeremiah Denton (R-Ala.), Sporkin's leading critic, has been granted four closed hearings on allegations that Sporkin improperly intervened in an FBI probe of a leak of classified Central Intelligence Agency information. Nearly a dozen witnesses have testified.

Denton recently demanded a fifth closed session to hear from the former CIA agent accused of the leak. But the hearing was canceled Tuesday after objections by an unnamed Republican.

A spokesman for committee Chairman Strom Thurmond (R-S.C.) said the panel may be unable to vote on Sporkin by next week unless the hearings are completed. If that happens, a committee official said, "The Democrats will go wild . . . . There will be war."

Joel S. Lisker, a Denton aide, said, "Sen. Denton has not been involved in any delaying tactics. What we have here are allegations that he deems serious . . . . We'd like to get the damn thing over with."

Lisker said Denton's probe has been hampered by a lack of cooperation from the Justice Department. He said the closed hearing has been rescheduled for next week and will be followed by an open hearing that will examine Sporkin's record as enforcement chief of the Securities and Exchange Commission, which Lisker said raises questions about Sporkin's "legal ability and judicial temperament."

The nomination is caught in a partisan feud in which Democrats have charged Republicans with rushing through dozens of conservative judicial nominees, yet stalling on Sporkin.

Few have questioned Sporkin's qualifications to be a judge. But many conservatives have said they dislike him because of his aggressive tenure at the SEC.

Initially nominated to the federal court here in June 1984, Sporkin has said he did nothing improper in the FBI probe and merely suggested that the accused CIA agent hire a lawyer. The 1982 leak involved documents passed to a Middle East concern.

Committee Democrats agreed two weeks ago to vote on appeals court nominee John Noonan, an outspoken antiabortion advocate, in exchange for a GOP promise that Sporkin's nomination would reach a vote by Dec. 12.

"Everyone is making a good-faith effort to try to finish this, but there continue to be outstanding issues," said Thurmond's spokesman, Mark Goodin. He said Thurmond believes that the final hearing "is a very important component to evaluate the nomination as far as Sen. Denton and perhaps some others are concerned."

While the dispute festers, committee Democrats have put a hold on the nine judicial nominees awaiting Senate action. Tentative agreement on allowing more time for judicial nominations, which would not affect Sporkin, was reached yesterday by the Democratic and Republican leadership, but committee members still must approve it.