There would be nothing remotely like it: the State of New Columbia, carved out of the tiny District of Columbia, no more than 57 square miles and the most densely populated state in the union.

It would boast no industry or agriculture to speak of, this first entirely urban state one-twenty-third the size of Rhode Island. The governor and state legislature would double as mayor and city council. New Columbia would operate with a special federal subsidy available to no other state. It would be the only state that could operate a major prison in an adjoining state without that state's permission.

And on the map, it would look less like some gleaming diamond, wedged between Virginia and Maryland, than like a slice of Swiss cheese, with holes left where the White House, Capitol Hill, the Supreme Court, the Mall and other federal facilities were excised from its territory.

Foreign embassies, the Naval Observatory and the vice president's mansion would be part of the new state, yet Union Station, Hains Point and Roosevelt Island would fall across the state line, part of a new federal enclave called the National Capital Service Area.

The debate over the political status of the residents of the seat of national power -- who now total nearly 630,000 -- is older than the Constitution itself.

The District, created out of land ceded by Maryland and Virginia, was envisioned by the founding fathers as a safe haven for Congress and the federal government, not dependent on any one state for security and services. Any state with the federal city in its midst would become a "super state," it was argued, the equivalent of a "Rome along the Potomac."

Yet for more than 200 years, politicians and legal scholars have weighed national necessity against individual liberties in defining and redefining the geographic and political parameters of the federal city.

This debate was joined once again this month when the House District of Columbia Committee voted 6 to 5 to send to the floor a bill that would grant the District statehood and full representation in the Senate and House. At present, the District has one nonvoting delegate in the House and no representation in the Senate.

The bill has been backed by House Speaker Jim Wright (D-Tex.) and Majority Leader Thomas S. Foley (D-Wash.), and it has a chance for passage this fall. But it is expected to encounter stiff opposition from Republicans and conservative Democrats in the Senate, where the Democrats hold a slender majority. The White House has hinted that President Reagan would veto the bill if it reached his desk.

Del. Walter E. Fauntroy (D-D.C.), chief sponsor of the statehood bill, who has presided over several years of hearings on the controversial proposal, contends that there is no legitimate constitutional or economic barrier to transforming the nonfederal portions of the District into the 51st state.

"There are answers to the questions which a few have raised in their effort to deny to the people of Washington what they insist upon for themselves," said Fauntroy, who once was an opponent of statehood. "It is wholly inconsistent to espouse the virtues of democracy around the world while denying democracy to three-quarters of a million taxpaying Americans in the nation's capital."

Rep. Stan Parris (R-Va.), the ranking minority member of the District Committee, argues just the opposite: that there are compelling constitutional arguments against statehood that take precedence over the voting rights of the District's residents.

Fauntroy has repeatedly cited generally positive testimony by several scholars, including that Congress could grant statehood to the District simply by passing a law and need not amend the Constitution or seek permission from Maryland.

Maryland ceded the 69 square miles that today make up the District. Originally the District included 100 square miles, but Virginia reclaimed its parcel in 1846.

"All of the other steps that have been taken in the past in connection with admitting new states into the union are informal and quite variable," George Washington University law professor Peter Raven-Hansen said. "They emerge from practice rather than constitutional requirement."

But Reagan administration lawyers, along with four Republicans and a Democrat on the House District Committee, have argued that the statehood bill is seriously flawed and conflicts with a number of sections of the Constitution, including Article 1, Section 8, Clause 17, which grants Congress "exclusive" legislative authority over the District.

In testimony in April, Assistant Attorney General Stephen J. Markman argued that enactment of statehood legislation would be "inconsistent with the federal system as it has existed for the past 200 years." He said the disenfranchisement of District residents was neither a mistake nor an oversight but an integral part of the original constitutional plan.

And scholar Stephen A. Saltzburg, professor of constitutional law at the University of Virginia, testified before Fauntroy's subcommittee that Maryland's views on statehood must be taken into account. Rep. Ronald V. Dellums (D-Calif.), chairman of the District Committee, allows that the Maryland issue is not open and shut, and he has instructed committee staff members to talk to Maryland officials about their position.

The founding fathers' obsession with establishing a safe, secure federal enclave stemmed from the so-called Philadelphia Mutiny of June 1783, a traumatic incident at the close of the Revolutionary War in which a band of 80 disgruntled Continental soliders marched from Lancaster, Pa., to Philadelphia demanding back pay. The rowdy, ragtag group surrounded the statehouse (now Independence Hall) and threatened members of Congress, who asked for help from Pennsylvania authorities -- and were turned down. Finally, the harassed members of Congress fled town.

Within weeks, James Madison was appointed to head a committee seeking a permanent, secure seat for the national government. Four years later, in 1787, Congress resolved to exercise exclusive control over all legislation affecting a District, not to exceed 10 miles square. On June 28, 1790, Congress chose the current site.

As the District grew from a tiny village of 3,200 people in 1800, Congress experimented with a variety of local governments, beginning with an appointed mayor and elected city council, then a territorial government with a governor and legislative assembly, later an appointed board of commissioners, and then an ap- pointed mayor and city council.

Since 1974, the District has operated under a home rule charter that leaves Congress with ultimate veto power over the city's legislative and budgetary affairs. Residents are entitled to elect their mayor, 13-member D.C. Council and school board.

In 1978, Congress passed a constitutional amendment that would have given the District voting representation in the House and Senate, but it died in 1985, having received the approval of only 16 of the necessary 38 state legislatures. It was then that Fauntroy, a champion of the failed amendment, climbed on the statehood bandwagon.

The proposed New Columbia would have a larger population than Alaska, Delaware, Vermont or Wyoming. It would be by far the most densely populated state in the nation, with 13,900 people per square mile of nonfederal land.

The Reagan administration and House Republicans contend that the District lacks the requisite natural and economic resources to stand on its own. They cite the District's dependence on an annual federal payment from Congress, as compensation for local services rendered, that totals $425 million this year, or about 18 percent of total city revenue. Fauntroy's bill calls for a continuation of the federal payment.

Statehood proponents point out, however, that the federal payment has declined steadily as a percentage of the overall D.C. budget and that city residents pay about 83 percent of the costs of running the local government. Economist Andrew F. Brimmer studied the issue and concluded that the new state is viable given a continued federal payment and a "commuter tax" on wages earned in the District by nonresidents.

Fauntroy's bill would allow the state to continue operating Lorton Reformatory in neighboring Fairfax County, on federal land, without the approval of the State of Virginia. The D.C. prison complex for years has been troubled by overcrowding, escapes and violence.

"It's like having your cake and eating it too," said Rep. Romano L. Mazzoli (D-Ky.), the only Democrat on the House District Committee to op- pose the statehood legislation. "New Columbia wants all the {old} benefits of a federal payment and keeping {Lorton} . . . yet it wants all the rights of a state. I don't know if you can have it both ways."

The precise boundaries of the pro- posed state, an issue of extreme im- portance, received little attention during the markup of the bill. But a number of sites in which the federal government has considerable interest, including the vice president's residence and Washington's foreign embassies, would be outside the fed- eral enclave -- a fact likely to provoke controversy.

Said Paul W. Whipple, a retired District official and political scientist, "Saying there are no constitutional or serious practical impediments to statehood is outright deception."