District of Columbia Mayor Marion Barry and Del. Walter E. Fauntroy lobbied here today for the D.C. voting rights amendment and changed Gov. Harry R. Hughes' mind from leaning against the measure to leaning in its favor.

Five days ago Hughes said he had "some problems" with the constitutional amendment because it would give the District two U.S. senators. This right is normally reserved for states. But after a 30-minute meeting in the governor's office today with Fauntroy, Barry and D.C. City Council Chairman Arrington L. Dixon, Hughes said, "from the standpoint of shading and degree, I'm going the other way."

Less than an hour earlier, Fauntroy made an ally out of Sen. Edward T. Conroy (D-Prince George's), who chairs a committee that will cast the first vote on the amendment. Conroy, who has been ambivalent on the issue, said he was so impressed with Fauntroy's testimony before his committee that he was now partial to the delegate's position.

"You're tending to persuade me to lean that way," said Conroy, whose support of the measure would assure smooth passage through his committee and give supporters of the amendment an influential spokesman on the Senate floor.

Conroy, like Hughes, said he put aside his original reservations after hearing Fauntroy argue that the District's 700,000 taxpaying residents are entitled to "this basic citizen right to be represented in our national legislature."

Making friends with such influential figures as Hughes and Conroy signigicantly boosts -- though far from guarantees -- ratification of the controversial amendment that would give the District two senators and at least one member of the House of Representatives, in place of today's one non-voting member of Congress.

To become effective, the amendment must be ratified by 38 state legislatures within seven years of last summer's approval by Congress, and supporters of the measure are counting on Maryland to become the fourth state to back the proposal. So far, New Jersey, Ohio and Michigan have ratified it, four other states have rejected the measure and one state has postponed action.

Even with the support of key political figures here, the amendment is expected to encounter stiff resistance from an unusual coalition of rural lawmakers opposed to the growing power of an urban center, Republicans who fear extra representation from the predominantly Democratic District of Columbia and suburban Washington legislators who are worried about a commuter tax.

The hope of ratification in this 90-day session rests in large measure with the delegations from Prince George's and Montgomery counties, many of whose members are seeking a "moral commitment" from District leaders not to try to impose an income tax on Marylanders who work in Washington, if the amendment passes.

The Home Rule Charter of 1973 prohibits the District from levying such a tax without authorization of Congress.Opponents of the measure from the Washington suburbs -- whose senate delegations appear to be evenly split on the issue -- argue that the chances of getting the needed approval for a commuter tax would gain if the District were given voting members in both houses.

"I am unwilling to take the risk of causing additional taxes to be levied upon Maryland citizens," said Sen. John J. Garrity (D-Prince George's), who has sponsored a bill that would postpone a vote on the amendment until after a 1982 referendum could be conducted.

Fauntroy fielded questions about a possible commuter tax throughout the day, saying he could not promise legislators that the 165,000 Marylanders who work in Washington -- about a third of the work force in Prince George's and Montgomery -- would remain free from an income tax if the amendment were ratified.

He maintained, however, that fears of a commuter tax were exaggerated -- the District representatives would hardly tip the balance in favor of authorization -- and cloud the real issue: whether Americans will "continue to espouse the virtues of democracy to the world and halt that democracy at the borders of the District of Columbia."

"We have before us a basic moral question," Fauntroy asserted in an afternoon debate against U.S. Rep. Robert E. Bauman (R-Md.). "The question is whether we are going to remain true to our Democratic principles. I hope you (the Maryland legislature) will seize the high ground of principle."

Bauman, the conservative congressman from Maryland's Eastern Shore, said he opposes the amendment because it would give the District full rights of statehood even through the U. S. Constitution held the District to be a "nonsovereitn entity." Giving Washington full representation in Congress, he said, would set a bad prededent for U.S. territories who would then want similar rights.

Opponents of the measure will appear before Conroy's Constitutional and Public Laws Committee on Wednesday.