"Give me your tired, your poor, your huddled masses yearning to breathe free . . . " and we'll ship them to New Jersey.

In the shadow of the Statue of Liberty, two states are trading barbs across New York's harbor. Overwhelmed by a surge of homeless families, New York City is housing about a thousand of its most destitute citizens in New Jersey hotels. The Garden State is less than thrilled.

"Dealing with the tragic problem of homeless people by shipping them to a neighboring state is the height of irresponsibility," said New Jersey Gov. Thomas H. Kean.

Rep. Frank J. Guairni (D-N.J.) called it the "Kochlift," likening it to Cuban President Fidel Castro's refugee boat lift, and is demanding a congressional investigation.

But in New York, the increased numbers of homeless and an ever-worsening housing crunch have created a major crisis. Mayor Edward I. Koch says no accommodations are available, though the city is still looking.

"I am not seeking to quarrel with Gov. Kean, whom I consider a friend, and I don't think the people of New Jersey want to pass a law which forbids New Yorkers in emergency situations from living temporarily in their state," Koch said.

"It is not like we are shipping people there on a permanent basis or giving them a subway token and saying, get out of town."

The National Coalition for the Homeless estimates that as many as 2 million Americans are homeless. The problem is particularly acute in New York, which is under court order to provide clean and safe shelter for its huge homeless population.

Last year, about 60,000 homeless people passed through public agencies, including 20,000 members of families seeking housing, 20,000 homeless youths and 18,000 single adults in shelters.

In downtown Newark's Lincoln Motel, hard by the train tracks, Marion Trotman, 44, sat combing her granddaughter's hair today. A game show blasted from the television.

On the wall were two pictures of semi-nude women, reminders of the motel's previous guests. The aroma of turkey legs cooking on a hot plate in the bathroom filled the air.

"Where can I find an apartment in New York for $183 per month?" Trotman asked. "Where else can I go but here? On the streets?"

Trotman, who lives on welfare with her son Sean, 13, is allowed $183 a month to rent an apartment, the maximum for a family of two under rental allowances frozen since 1976.

By contrast, the city can spend $1,000 per month to put the Trotmans up in a hotel--because that falls under an emergency funding statute.

Trotman said she was evicted from a Staten Island housing project after she lost her job as a switchboard operator, and was sent to the Lincoln in Newark on May 2.

Until school closed June 26, Sean commuted almost three hours each way to his Staten Island junior high school, taking two trains, two ferries and two buses.

Sean, a track star who proudly displays his medals, says living in the hotel is boring. "There's nothing to do. At home, I'd have the track team."

Many of the homeless families being housed in New York and New Jersey hotels are victims of evictions. Others have been chased out by fires which have devastated large sections of the city.

But the biggest problems are skyrocketing rents and drastic cutbacks in federally funded housing projects.

"No new housing projects are being built," said Robert Jorgen of New York City's Human Resources Administration. "People who live in the current projects don't seem to be graduating. There is no federal money for public housing and the private market does not support the means of poor people."

As a result, he said, the number of homeless families in the city jumped from 950 last July to 2,000 today. Jorgen said Red Cross and city welfare workers began sending homeless families to New Jersey in February.

The number of families in New Jersey increased to 284 by last week, partly because New York's hotel owners began to rent more rooms to tourists.

The city is paying $33 per room to house families in two hotels in Newark, one in East Orange and one in Jersey City at a daily cost of about $10,000.

Local New Jersey officials claim that the New Yorkers are burdening voluntary organizations and government agencies. New Jersey social workers have had to handle 10 child abuse cases.

Pharmacists here will not honor New York's Medicaid cards, so the New Yorkers have had to obtain medicine from local hospitals.

Officials here worry that they will have to provide schooling for the New York children this fall.

East Orange Mayor Thomas H. Cooke Jr. on Thursday threatened to file suit against New York to halt what he called "the tide of refugees from New York's economic war zone." He said he would ask Rep. Peter W. Rodino Jr. (D-N.J.) to introduce legislation to prohibit the use of welfare money for relocating people across state lines.

All the bureaucratic wrangling is a mystery to Stephanie Davis, 22, an unwed mother from Brooklyn with three children.

Welfare officials allow her to spend $218 a month for rent--and for that, she can't find an apartment. After her third child was born, Davis had to move out of her sister's apartment, where she had been sleeping on the sofa with her two older boys. Welfare officials sent her to the Lincoln. "What I can't understand," she said, "is that the city can pay more than $900 a month for us to live in this hotel room. If they'd just give me $400 a month I could rent an apartment in New York."