Although his intentions are far more loftly, Rep. Edward Koch after his election as mayor of New York next Tuesday will be reduced to the same demeaning role as defeated Mayor Abraham Beame: a mendicant seeking federal largesse to keep alive the nation's greatest city.

That is the message of a speech drafted last week for later delivery by financier Felix Rohatyn, who has spent the last two years trying to settle the city's chaotic financial affairs. His conclusion: "The city cannot do much more, on its own, to stimulate its economy and improve the quality of its life." The help must come from Uncle Sam.

Koch and his advisers agree (though, of course, they do not use Rohatyn's blunt language). Thus, Koch must follow Beame's path in begging from a reluctant administration and hostile Congress. While Koch is vastly more credible in Washington than his predecessor, his chances for success are not much better.

That Koch becomes mendicant-elect as well as mayor-elect Nov. 8 is sadly ironic. No modern mayor of New York has taken office with fewer obligations to labor unions or political clubhouses or with a better understanding of what is needed after decades of profligacy - a tight budget, lower taxes, less government.

On his uphill climb to the Democratic nomination virtually assuring him the election, Koch proved that organized labor's upport is no more necessary here than the crestfallen Democratic organization's. Having campaigned in the primary by promising tough bargaining in city labor negotiations, Koch told a post-primary meeting of municipal union leaders: "I don't owe anything to anybody."

Nor has he changed his tuned with the advent of victory. "Municipal employees cannot be expected to bepaid wages in excess of the private sector," Koch told us, adding "I do not believe anyone can be kept on a job who is not needed." That promises not only hardnosed wage negotiations but some job layoffs as well.

Yet, Rohatyn's draft speech argues that the forthcoming struggle between city and union resembles "convalescents fighting over the crumbs." Rohatyn, head of the Municipal Assisitance Corporation (MAC) set up to keep the city from bankruptcy, paints a bleak picture. Even with no municipal wage increases at all (which is not possible), the $400-million city-budget deficit would remain. How, then, to reduce taxes to stop the business exodus?

President Carter has the solution, suggests Rohatyn. The financier's draft speech says the President must redeem "a solemn pledge" made during the 1976 campaign to ensure the city's welfare costs (variously estimated at between $600 million and $1 billion a year).

Herein lies the grand strategy of Rohatyn and Gov. Hugh Carey during the Ford administration: Get just enough help from the Republicans to survive until the election of a Democratic President, who would then push through a federal welfare takeover. Carter's failure to do this has bred bitter disappointment reflected in Rohatyn's draft speech: "Without a redemption of [Carter's] pledge, the pain and the suffering would have been an empty charade, a theater of the absurd, for this city cannot survive under this burden.

"I think Felix is overly pessimistic," a top Carter administration official told us, suggesting that two years of fighting off bankfuptcy have given the monitors from MAC battle fatigue. This official feels the city budget deficit can be closed with neither draconian cuts in services nor a federal welfare takeover.

The hard fact is that the Carter administration has no intention of picking up the city's welfare tab. The Carter welfare-reform program ("It's a terrible bill," Koch told us) provides nothing until 1981. At this writing, Sen. Daniel Patrick Moynihan (D-N.Y.) and the White House are near agreement on a compromise for immediate relief of less than $200 million.

But even that sum, inadequate by Rohatyn's standards, faces a hazardous course in Congress. Despite what Koch calls "the collegial spirit" of his old friends in the House and despite of his far greater credibility than Beame, he may prove no more successful a mendicant. Congressional hostility toward special treatment for New York is overwhelming.

These realities might well dampen Koch victory celebrations on Tuesday. Having risen from obscurity to defeat the power brokers, Koch now must confront the labor unions knowing that succes there cannot save the city. Instead, Ed Koch must go to Washington begging for help. Thanks to the mindless excesses of his predecessors, he cannot be optimistic about succeeding in this wretched task.