Plans for a convention center in downtown Washington were dealt a severe and possibly crippling blow in the House yesterday when Rep. Robert E. Bauman (R-Md.) single-handedly blocked the city government's continued right to borrow construction funds from the U.S. Treasury.

Depending upon what happens at the Capitol during the next two weeks, the action could lead to killing the convention center for this year, or it could create only a minor delay for the $110-million project.

Also affected by yesterday's action, probably temporarily, are another $83 million in schools, transit, library and other construction projects that also would be financed by Treasury borrowing.

The convention center was expected to win unchallenged House approval as part of the District's $1.4 billion budget for the 1978 fiscal year, which starts Oct. 1. The budget, minus the Treasury borrowing power, was approved yesterday by a vote of 298 to 64.

The amount of Treasury borrowing eliminated by Bauman's action totals $110 million. Of this, $27 million was earmarked as start-up costs for the convention center project.

Despite the advent of District home rule in 1975, the city's annual budgets still must follow the same seven-step process through Congress as the budgets for the departments of the federal government.

The Senate has yet to act. The center project faces an uncertain future in that chamber, where the Appropriations Committee voted 13 to 7 on Thursday to block it. For final approval, both chambers must grant their support.

A legal quirk resulting from the shift to home rule gave Bauman the muscle that permitted him to block the continued borrowing authority yesterday.

Under the old form of city government, with most real power exercised by the White House and Congress, the District routinely borrowed funds each year to pay for its congressionally approved construction projects. The money was repaid over 30 years, with interest.

With the advent of home rule the Treasury borrowing power legally expired. The new charter called for the city to float municipal bonds, like other cities do. But the city's finances were in disarry, and the Congress told the city to hold off on trying to sell bonds.

To cure this, Congress has included a stopgap clause in the District budget for each of the past two years granting the continued power to borrow from the Treasury. If anybody had challenged that clause on the House floor, it would have automatically killed the borrowing power. House rules prohibit the makingof legislative policy in budget bills.

Bauman, a foe of the convention center who has assumed a role as a conservative watchdog on the House floor, issued such a challenge yesterday.

Rep. William H. Natcher (D-Kv.), chairman of the House District Appropriations Subcommittee and floor manager of the budget bill, capitallated. But he contended Bauman's victory would be only temporary.

Ironically, a separate bill extending the District's power to borrow from the Treasury until Oct. 1, 1979, has been pending on the House calendar since May 5. If it had been passed, it would have been unnecessary to put the challenged clause in the District budget bill.

But Rep. Charles C. Digg Jr. (D-Mich.), chairman of the House District Committee, did not call it up for action until it was too late. It was on the House calendar for a vote last Monday, but it got shoved aside for national legislation, and is not scheduled to be voted upon until Sept. 26.

Bauman told reporters yesterday that he will try to defeat that bill when it is brought up.

Yesterdys' action left the center project and the city's borrowing power in a position of parliamentary uncertainty and confusion.

The action also brought forth a torrent of House debate on both the center and on city finances, but only after Bauman already had won his point.

Natcher and his subcommittee's senior Republican, Rep. Clair W. Bruguner (Calif.), contended the center is needed as a stimulus for renewal of the area around its proposed site at Mount Vernon Square, north of downtown, and that it would produce jobs and tax revenues. Del. Walter E. Fauntory (D-D.C.) agreed.

Bauman depicted the center as a loser that both city and national taxpayers would have to bail out.

Rep. Stewart B. McKinney (R-Conn.), senior Republican on the House District Committee, portrayed the situation more broadly.

Congress governed Washington for more than a century, McKinney noted. "We ran the city into whatever condition it is in," he said. "We just recently said (to its citizens), 'here it is back, pay for it.' . . . I would suggest the city deserves a break."

Whatever the fate of the convention center when the bill moves through the Senate, that chamber's action seems likely to preserve other construction projects knocked out in the House by Bauman's action. Those projects inlucde $56.7 million for the new Mount Vernon Square campus of the University of the District of Columbia and a new $35 million municipal office building.

At the District Building, the House action was met with disappointment but generally with confidence that the damage will be repaired.

"This again shows why we need (full) home rule," Council member Marion Barry Jr. (D-at large), said.

"These little jive people in the House mess with our lives and they're not paying for anything . . . It just makes it difficult for us to run the city when we have to keep reacting to the Congress."