After weeks of headlines and controversy, the FBI and congressional investigations into how Ronald Reagan's presidential campaign obtained Carter White House documents in 1980 are showing few signs of progress.

At this point, FBI investigators do not have enough evidence to build a criminal case and few leads that would point toward one, according to sources close to the investigation.

Where investigators have indications of a crime, such as the possible removal of classified documents, they cannot prove who removed the material, the sources said. Where they know who was involved, such as Reagan campaign officials who recall receiving Jimmy Carter's briefing papers for his presidential debate with Reagan, they do not have the necessary elements for a criminal prosecution, according to the sources.

They said some investigators believe the entire episode has been blown out of proportion and the probe may stall unless there are new disclosures in the press or from the congressional inquiry.

But the House subcommittee, chaired by Rep. Donald J. Albosta (D-Mich.), has interviewed only a dozen witnesses and is weeks away from questioning any of the senior Reagan administration officials involved in the case. The subcommittee has been hampered by inadequate staff, partisan internal disputes, questions of jurisdiction and an impasse with the White House over access to Justice Department records and Reagan campaign files.

Even some Democrats on the subcommittee are doubtful.

"I'd be surprised if our committee found any fireworks," said Rep. Douglas H. Bosco (D-Calif.). "We don't have seasoned investigators. Wherever they've gone, they've found the Justice Department has already been there."

The Albosta probe has been inching forward since it began five weeks ago. By contrast, five weeks after allegations surrounding the Environmental Protection Agency surfaced last February, the issue had generated so much criticism in Congress and the media that Administrator Anne M. Burford was forced to resign.

A number of influential environmental groups eagerly fanned the flames of the EPA controversy, but there is not now a comparably strong movement for election campaign reforms. Five Democratic House chairmen rushed to investigate the EPA, but no one has joined the debate papers probe by Albosta's small Post Office and Civil Service subcommittee on human resources.

The Justice Department's track record in the EPA investigation also suggests the difficulties of prosecuting such cases. After nearly six months of investigation, Justice Department officials have not brought any indictments against an EPA official, except for a contempt of Congress charge against Rita M. Lavelle, who was acquitted by a U.S. District Court jury Friday.

Since President Reagan called in the Justice Department, FBI agents have been methodically interviewing people from the Carter and Reagan campaigns, but they have not been working overtime or on weekends.

Sources close to the investigation said most of the people questioned by the FBI are those already named in media accounts, as well as callers who are volunteering theories of campaign wrongdoing. The sources said it may be difficult or impossible to prove criminal intent if the Carter briefing papers were leaked by a disgruntled Carter aide who legally had access to the material, unless the person was promised a job or some other inducement.

While the FBI originally was given a narrow mandate, Justice Department officials said they are free to follow new leads into such areas as suspected leaks from Carter's National Security Council and intelligence gathering efforts by the Reagan campaign.

Investigators are said to have become interested in internal Reagan White House documents assembled during its brief investigation into how the Carter papers got into the files of Reagan campaign officials. The Albosta panel also has been seeking these Reagan White House documents.

Not much has moved quickly for Albosta since he received responses to his June 15 inquiries, in which White House chief of staff James A. Baker III said he got the Carter briefing papers from CIA Director William J. Casey and Casey maintained he had never seen the material.

"Albosta has contributed one major fact to this investigation--that's the conflict between Mr. Baker's assertion and Mr. Casey's denial," said Christopher Matthews, a spokesman for House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), who has been openly skeptical of the panel's inquiry. "That remains at the heart of the matter."

The Albosta subcommittee has struggled for weeks as its three-person staff, headed by Micah Green, 25, worked round the clock. The few phone lines in their cramped office remained busy as they also prepared for scheduled hearings on civil service issues.

"We haven't done as much investigating as we should have, but we've had a skeleton crew," Albosta said.

The panel recently added two staff members from its parent committee, hired former Watergate investigator James Hamilton as special counsel, and sought help from the General Accounting Office. The expanded staff plans to question 60 to 70 more people in the coming weeks.

"We're building an effort," said one subcommittee official. "That's why it may seem like there's been a lull. But you'll see the pace picking up now. We had to cram three months of work into a couple of weeks."

Another problem is that the subcommittee has based its probe on a thin jurisdictional reed--that of revising the 1978 Ethics in Government Act--and had to write special guidelines for the investigation. This enabled Rep. Benjamin A. Gilman (R-N.Y.) to argue for tightening the ethics law without searching for a "guilty culprit."

Albosta also lacks subpoena power. He must instead rely on the chairman of the parent committee, William D. Ford (D-Mich.), who has so far been unwilling to subpoena documents. The administration, meanwhile, has offered to give Albosta only those Reagan campaign records that the FBI deems relevant.

The key question is whether a majority of the House would vote to enforce a subpoena if the administration continues to resist.

"I'm not sure there's been a lot of public pressure to pursue this thing," Rep. Bosco said. "Given the House leadership's opposition, the White House is well advised to string this thing out."

Administration officials do not plan to argue that campaign papers are shielded by executive privilege. But they could challenge any subpoena as overly broad or question the panel's jurisdiction over campaign aides who were not federal employes.

Albosta insists he is not interested in material unrelated to the unauthorized transfer of documents, but the administration appears determined to prevent him from obtaining peripheral material that could prove politically embarrassing.

"Our goal, obviously, is to get this thing resolved as soon as possible," said one White House official. "But we kept coming down to the same impasse--their willingness to look at the Carter files as well." Albosta has refused a White House offer of access to Reagan campaign files at Stanford University's Hoover Institution if he agrees to inspect all Carter campaign records as well.

This official said the dispute could set a precedent by which the winner of a future presidential race could use the government's power to investigate the loser's campaign.

He said the campaign files, for example, might contain advice from a disaffected Chicago Democrat telling the Reagan camp to focus its efforts on certain election precincts. "I can think of 20 more examples like that which have nothing to do with . . . an illegal transfer of documents," he said. "It's the meat of the campaign."

An administration official has said the White House also is concerned about the unearthing of Reagan campaign strategy documents that could be embarrassing to a president seeking reelection, even though unrelated to the ongoing investigation.

O'Neill aide Matthews predicted that "a month from now the issue will fade, but the cloud will remain. The administration is willing to put up with the cloud . . . because they must think the storm would be worse. They could cut their losses and take the heat and it'd be over in two days. That is, unless they have to admit to theft or receiving stolen goods."