When Robert L. Johnson, president of District Cablevision Inc., signed an agreement in February to build a $130 million cable television system here, he knew that the investment market had twice rejected the proposal and that two of the nation's largest cable operators had said the project could not be financed without modifications.

At the signing ceremony with city officials, Johnson held up a shiny red apple as a symbol of the no-frills, state-of-the-art system he promised to build, but he offered no clues to the financial problems that lay ahead.

Johnson had promised the city that his firm "would not be back seeking relief from promises we could not keep." But today he says it will be impossible to undertake the long-awaited city-wide cable project without $32 million worth of concessions.

Johnston, Lemon & Co., a local investment house retained by District Cablevision to seek financing since last July, says it had "intense discussions" with eight investment firms in an effort to help District Cablevision raise $30 million through a limited partnership offering.

Yet a vice president of one of the New York firms contacted about financing said he had only preliminary discussions with District Cablevision officials.

"They never asked us to evaluate the economics of the proposal," said Steven Rattner of Morgan Stanley & Co. "It amounted to a couple of quick phone conversations. But a limited partnership is almost certainly not something we wanted to do."

District Cablevision is one of many companies throughout the country that promised more than they could deliver or encountered serious financial problems in urban areas and then sought to scale back their promises.

Industry analysts say that uncertainties surrounding President Reagan's recent tax reform proposal also have discouraged potential investors in cable television projects.

District Cablevision counted on the presence of two of its shareholders, cable operators Tele-Communications Inc. (TCI) and United Cable, to provide the company with clout in the investment community, despite warnings from executives of both companies that the proposal was not economically viable.

Meanwhile, the city's goal to have a local minority-controlled company like District Cablevision build and operate the multimillion-dollar project now appears to be in serious doubt.

Denver-based TCI, the nation's largest cable operator and a 20 percent shareholder in District Cablevision, is prepared to step in and put up $30 million or more to get the cable project under way, according to company officials.

"If a major company has that kind of financial stake in it, then as far as I'm concerned they are an owner and maybe the major owner," said Carl Pilnick, a California-based cable consultant who served as the District's cable expert throughout the franchising process. "The real evidence of ownership and control will come after things settle down."

Johnson, a political supporter of Mayor Marion Barry dating to 1978, and officials of TCI insist that District Cablevision will remain in control of the project if the City Council grants concessions sought by District Cablevision and endorsed this week by the mayor. Those changes include reducing the number of residential channels from 78 to 54 and delaying payments the firm must make to the city.

District Cablevision did not own or operate a cable television system before it was awarded the D.C. franchise by the City Council.

"We had no assurances at all that we could raise the money," Johnson acknowledged recently in reviewing events that led to the current contract crisis. " . . . We knew it was going to be tough, but we didn't know it would be impossible."

James R. Kleeblatt, an official with Johnston, Lemon & Co., said his company held serious discussions with eight investment banking firms, most based in New York, in a futile effort to get the firms to help sell or invest in a limited partnership offering.

"We met with total rejection on their willingness to try to help us sell an offering," said Kleeblatt. "There is no sense in going through the steps of making and offering if no institution or individual is interested in buying."

The mayor this week sent a letter to the City Council outlining his recommendations for changes in the cable franchise agreement and urging the council to act before it begins its summer recess next month.

District Cablevision sought support from Barry to eliminate a requirement that the firm wire the entire city for cable television, but the mayor said he was committed to making the system available to all residents.

However, Johnson said yesterday that the absence of that provision could "make or break" any modified agreement. He said District Cablevision must have some provision allowing it to seek relief if the company experiences financial problems or is not receiving a resonable rate of return.

"We don't think we should go bankrupt to wire every home in the city," he said.

Of the three firms that bid on the city's 15-year cable franchise, District Cablevision appeared to have the most politically influential group of shareholders and backers -- including many with close ties to Barry. The company also scored points with some City Council members by teaming up with the Chesapeake & Potomac Telephone Co., which agreed to build, maintain and own the cable transport lines as a cost-saver.

Now, Johnson, a former press aide to D.C. Del. Walter E. Fauntroy and a worker in Barry's first mayoral campaign, is banking on his ability to persuade enough council members to go along with the proposed modifications.

While most City Council members say they are reluctant to seek new cable bidders, some are angered by the request for concessions and believe they were misled by Johnson's firm.

City Council member Betty Ann Kane (D-At Large), chairman of the cable television committee, also questioned whether District Cablevision worked hard enough in seeking financing. "I need to be convinced that they really did try to get financing and couldn't," she said. ". . . [District Cablevision] has a very bad business sense and a very bad PR sense."

District Cablevision's request for changes in the franchise agreement raises many questions about the prospects for cable television in the District, including the timetable for construction, the scope of the system and the ultimate role of TCI.

TCI owns, manages or has investments in 700 cable systems that have a total of 3.6 million cable customers. The company had $1.6 billion in assets and $449 million in revenues in 1984.

TCI also owns 16 percent of Black Entertainment Television (BET), a cable satellite network that is headed by Johnson. John Sie, vice president of TCI, said recently that his company intends to honor District Cablevision's current controlling role in the project.

"We're trying to help Bob [Johnson]," Sie said. "We're one of the founding members of BET, and we would like to see Bob succeed."

Ironically, one of the letters that District Cablevision submitted to the City Council to justify its proposed modifications appears to support the views of critics that TCI will gain control of the system.

John D. Field, the division manager for investments of American Television & Communications Corp., a cable system operator second only to TCI in size, said in a letter that District Cablevision needed modifications to obtain financing and that any major investor would want a signficant role in controlling the system.

"Any investor or group of investors providing equity capital must have ownership control of the system reflective of the equity contributed and risk involved," Field wrote. "Without that, no sane major cable investor will fund the equity necessary to build a major urban cable system."

Albert Giannotti, TCI's mangager of cable investments, said that if TCI becomes the chief limited partner for District Cablevision, the two companies will reach an agreement containing covenants and performance requirements to protect TCI's investment CAPTION: Picture, ROBERT JOHNSON . . . seeks $32 million in concessions; Chart, District Cablevision Inc., original proposals, franchise agreements, amended proposals.