The last congressional obstacle to the construction of a convention center in downtown Washington was removed yesterday when Sen. Patrick J. Leahy (D-Vt.) announced that his Senate D.C. Appropriations Subcommittee will offer no further objections" to the $99 million project.

A convention center here has long been the dream of many of the city's political and business leaders, who have contended that it would help keep the city economically healthy and competitive by attracting tourist and covention dollars and spurring economic redevelopment downtown.

Leahy, who had single-handledly held up approval of the center until he was satisfied that it would not be an economic drain on the city, did not try to conceal his continuing doubts when he made yesterday's long-awaited announcement.

"It is still my view that the proposal is marginal in an economic sense." Leahy said at a news conference at the Capitol. "If I were a citizen of the District of Columbia I would vote against it" if given the chance.

Nevertheless, Leahy said that private developers had covinced him that public financing of the center will stimulate sufficient related business development so that "the project should break even and not result in an added tax burden" to either District residents or other citizens.

Even opponents of the project appeared satisfied that Leahy either had imposed enough restrictions on the development to ensure that it actually would break even, or had given them enough time to force the question on the ballot next spring.

City officials and developers greeted Leahy's decision with jubilation.

Mayor Walter E. Washington, who was notified of Leahy's decision before the formal announcement, said he would "direct my staff to move ahead immediately with the next steps - land acquisition, relocation work, final design and site prepartion."

James T. Lynn, president of the Federal City Counil, said the center would provide "the one link we need" to fill the gap between tourists and visitors who come here to do business with the government.

Harold Walker, chief of the city budget office's capital improvement program, said it will take 18 months to gear up for a groundbreaking, and be ready for its first convention by the fall of 1982.

The center is planned for a site south Mount Vernon Square bounded by New York Avenue and H, 9th and 11th streets NW. The area has been the focal point of several development plans, including the proposed site for the downtown campus of the University of the District of Columbia.

After Leahy balked at original plans for a $110 million project, which he called "a lousy idea," the city came back with revised plans for a smaller, cheaper center. The two-level concrete structure, with a main entrance on 9th Street, is intended to attract 390,000 new convention visitors annually to the city, which already is the third biggest convention area in the nation. The center would have 225,000 square feet of space in two exhibition halls, and when not in use for convention, could seat 10,000 to 12,000 persons for civic events.

The main problem which Leahy said has been resolved to his satisfaction, was whether construction of the center would spark enough related private development to cover the $7.5 million annual loan payment that the city would owe to the federal treasury for advancing construction money.

The project has been touted by city officials as a catalyst for sorely needed employment. A study by the D.C. Manpower Department estimated as many as 4,000 new jobs might be created from construction of the center and hoterl restaurant and retail developments.

Two special taxes already are being collected by the District - a hotel room occupancy tax and a 10 percent surtax on corporations and unincorporated business incomes - to pay the $214 million cost of acquiring land on the site and related expenses.

Leahy insisted that the spin-off developments that could be directly attributed to the center generate enough new tax money to cover costs of repaying the other $773 million that the city would borrow from the federal treasury, to be repaid at $75 million a year over 30 years.

"I have not been overwhelmed" by the evidence presented at two public hearings last month, Leahy said yesterday, "but it appears the new project should break even."

The testimony that was "most useful" to Leahy, the senator said, came from Edwin K. Hoffman, chairman of the board of Woodward/Lothrop's department store.

Hoffman responded to the question Leahy asked of all potential developers- whether they would proceed with their proposals without a convention center - by saying construction of the center would "increase the probability of his proceeding by 45 percent."

Hoffman testified that he would recommend to the board of his publicly held company that Woodies invest $18 million for a new North Store at its downtown location and participate in development of $105 million of additional office and commercial space if the center were built.

Leahy said he studied other promised developments with Hoffman's probability facts in mind to reach the conclusion that approval of the convention center would have "a positive influence" on enough new developments to produce tax revenues needed to pay the entire annual fixed costs of the center.

Some of the other planned projects that contributed to Leahy's decision included a 200-room addition to the Quality Inn on New Jersey Avenue; additions to the Burlington and Fairfax hotels; a new Holiday Inn retail-office complex at 500 C St. SW; conversion of the Annapolis Hotel at 11th and H streets into a 500-room convention hotel; construction of a new 500-room hotel across the street from the center; and a promise by George Washington University to develop office and retail space on its vacant property on H Street between 13th and 14th.

Leahyt was able to hold up the project because as chairman of the five-member subcommittee, he held the proxy votes of the other two Democratic members, Sens. Dale Bumpers of Arkansas and Dennis DeConcini of Arizona. The two Republican members, Sens. Charles McC. Mathias Jr. of Maryland and Lowell P. Weicker of Connecticut, favored the original, larger proposal.

Leahy said he called all members of the committee before yesterday's announcement and reported to them that "it appeared the approval criteria (laid down by Leahy) had been met."

"The onus now fails to the business community to live up to their end of the bargain," Leahy concluded.

He added that "if the matter is put to a voter referendum, the subcommittee will assist the city to implement the demonstrated will of the voters, whichever way they go."

Jack Phelan, one of the opponents of the center who had met with Leahy earlier in the day, said he interpreted that statement to mean that if the center is approved by the voter, Leahy will not interfere. But if it is rejected, Leahy will not permit the city to go ahead with construction, Phelan said.

Opppnents who have formed the Convention Center Referendum Center are confident they can get the needed signatures to put the question to a vote. A poll of 762 registered Democrats in August by The Washington Post showed that 54 percent of those interviewed favored building the center, 33 percent were opposed and 13 percent were undecided.