The center of attention in the Senate dining room yesterday afternoon was the table where Del. Walter Fauntroy (D-D.C.) lunched with the Urban League's Vernon Jordan, Gary, Ind., Mayor Richard G. Hatcher, D.C. City Council Chairman Sterling Tucker and hardware store executive John Hechinger. Senator after senator wandered by that table offering their opinions on the upcoming vote.

"If we can hold Weicker and Schweiker, we'll be okay," said Sen. Edward W. Brooke (R-Mass.), referring to the potential swing votes of Lowell Weicker Jr. (R-Conn.) and Richard S. Schweiker (R-Pa.).

Sen. Thomas F. Eagleton (D-Mo.) said that Weicker - who was wavering on whether it was constitutional for a nonstate like the District of Columbia to have two senators - "can be a grumpy sort of a fella." (Weicker and Schweiker ultimately split - Weicker voting yes and Schweiker no - when the Senate voted 67 to 32 last night for the constitutional amendment to give the city voting representation in the House and Senate.)

"You've got two votes to spare, that's the Leahy count," offered Sen. Patrick J. Leahy (D-Vt.), "so I can go home, right?"

"Oh no!" Fauntroy exclaimed with a hearty laugh.

Fauntroy, who has been the District of Columbia's nonvoting delegate in the House of Representatives for the last seven years, said the most trouble he was having in his lobbying yesterday was collecting votes from senators from states "with less population than D.C. - Montana, Wyoming, Rhode Island."

Tucker mentioned that he felt one thing in favor of the proamendment forces was that Sen. William L. Scott, the conservative Virginia Republican, was leading the floor debate against the measure.

"I hope Sen. Scott continues to be their leader," Tucker added. "That's in our favor. He's a stumble-bum."

Throughout the day, Fauntroy darted in and out of strategy sessions in Vice President Walter F. Mondale's office just off the Senate floor, which was being used as a command center for proamendment forces.

Fauntroy used telephones there to call wavering senators and those who had not publicly announced their decisions on how they would vote. Then he would step outside the office into the Senate Reception Room to give instructions to aides or to lobby any senators passing through.

Before leaving home yesterday morning, Fauntroy said, he called Arkansas Gov. David Pryor, an old colleague of Fauntroy's in the House, to ask the best way to try to convince newly appointed Sen. Kancaster Hodges (D-Ark.) to vote for the amendment. Fauntroy said Pryor agreed to call Hodges, but Hodges eventually voted against the amendment.

The intensive lobbying for the amendment included the city's Democratic political establishment, which had been embroiled in the last weeks of a heated mayoral party primary, and many of the nation's key civil rights leaders, who traveled to Washington to help with the final push for passage of the measure.

Jordan, the executive director of the Urban League, talked to Weicker. Pro-amendment forces also accommodated the request of another senator, James R. Sasser (D-Tenn.), who wanted to have his picture taken with Coretta Scott King, widow of the slain civil rights leader. The Rev. Martin Luther King Sr. also greeted senators in the Senate hallways.

D.C. Mayor Walter E. Washington and Fauntroy, two sharp political antagonists in this year's Democratic primary in the city could be seen warmlly embracing each other in a common cause.The mayor, who had not been in the forefront of the lobbying effort for the amendment, said he sent letters urging passage to all 100 senators and made some telephone calls to senators.

The mayor said early in the day that after he talked to Sen. Lawton Chiles (D-Fla.), who was opposing the amendment, the senator "said he'd think some more about it since I called him. I moved him at least to a neutral." Chiles ended up voting against the amendment.

One of the mayor's chief opponents in the Sept. 12 primary, City Council Chairman Tucker, who is president of the proamendment lobbying group called the Coalition for Self-Determination, said he had talked to 40 senators in the last two weeks and 10 in the last 24 hours before the vote. He took credit for swaying Sen. John H. Chafee (R-R.I.) to vote for the amendment.

In sharp contrast to the proponents' lobbying tactics, the amendment's opponents talked quietly to their fellow Senate colleagues in the cloakrooms and on the floor.

Led by Sen. Scott, Orrin G. Hatch (R-Utah), Jesse A. Helms (R-N.C.), Paul Laxalt (R-Nev.) and James A. McClure (R-Idaho), the opposition was based mainly on what they said was the unconstitutionally of the amendment, Hatch said.

"If race had not been interjected into it, it would have been shot down a long time ago, because everybody knows it's unconstitutional," Hatch said. "But noboy wants to be accused of racism."

Hatch said that the floor leader of the pro-amendment forces, Sen. Edward M. Kennedy (D-Mass.), "has been very smart to make the issue one of blacks and whites." Hatch said he thought the charge of "acism against the opponents were unwarranted.

When debate on the measure began last week, Kennedy said he hoped that it would not be defeated just because two senators from the District of Columbia might be "too black, too liberal, too urban and too Democratic."

An aide of McClure's, who had worked closely on the antiamendment lobbying effort, conceded that the racial issue was the biggest stumbling block when opponents tried to persuade undecided senators to oppose the amendment.

A constitutional amendment to give the District of Columbia voting representation in Congress reached the floor of the House two years ago but fell 45 votes short of the two-thirds majority required to pass a constitutional amendment.