D.C. Mayor Walter E. Washington, City Council Chairman Sterling Tucker and D.C. Delegate Walter E. Fauntroy, who have had their political differences in the past, found a happy common ground yesterday.

The catalyst: the proposed and embattled Washington convention center, which has had its ups and downs on Capitol Hill, but which got three solid votes yesterday from the city's three top elected officials.

All saw the center as at least a partial remedy for some of the capital's economic problems, and lauded the House action Monday that would give the city borrowing power to get the project started.

Fauntroy, Washington and Tucker indicated that they would continue to lobby for the center, which would be built in the Mount Vernon Square area just north of downtown.

"We stand as a government of elected officials to say that we believe this is a high priority and we are encouraged by the action of the House, and we hope that the Senate will see this in the same way as we see it - as a matter of priority in the home rule context," Mayor Washington said.

The three officials said they were optimistic that the full Senate would approve the center, even though a Senate Appropriations subcommittee on the District omitted the project in its action on the 1978 budget request.

Fauntroy said he would step up lobbying efforts in the Senate to win that body's approval.

He added that there won't be any trade-offs "or deals" to set aside other budget requests to win Senate votes for the convention center.

Opponents of the center in both the House and the Senate have contended that the project could become a financial disaster and a burden that District and taxpayers elsewhere would have to bear.

But Washington, Fauntroy and Tucker stressed that the project would be a boon to the city economically and that the project had broad support among city officials, civic and religious leaders and businessmen.

"We have a good record on the repayment of our bills with respect to capital improvements," Mayor Washington said.

"We've built a new jail, a new court-house, $300 million worth of schools and we believe our record in meeting timetables is exceedingly good. We believe we can bring the civic center in accordingly he said.

Fauntroy said the center was needed because it could tap a valuable resource in the city - tourism.

"The members of the Congress know that we cannot expand our boundaries to meet our fiscal needs, they know that half the poperty in the city was taken off the tax rolls and that half the people who work here take the money, leaving no taxes here to deal with the services that we deliver," Fauntroy said.

Tucker said he was optimistic about approval of the project when it comes before the full Senate because of what he called traditional "yardsticks" he said Congress had used in the past on Council-approved legislation that has gone to the Hill.

Under the home rule charter Congress has 30 days to approve any legislation passed by the Council and signed by the mayor.

Tucker has said the vital questions are, "Is what the District wants to do possible under the Constitution, is it legal under the authority granted to the ciry under home rule, and is a substantial federal interest involved?"

He said that if the answers to the first two questions are yes and to the third no, "then the Congress ought to stay out of it."

"If they would apply that yardstick, they would quickly come to the conclusion that the decision is ours and would act on that decision in accordance with our wishes," Tucker added.