When the plump, naked model for one of Lucian Freud's paintings remarked that the artist "got value for money" because he "got a lot of flesh", she may not have realised how prophetic her words would come to be.

Last night, Freud's life-size portrait of Sue Tilley, a London Jobcentre supervisor, set the world record for the highest price paid in an auction for a work of art by a living artist.

At a Christie's auction in Manhattan, Benefits Supervisor Sleeping, which depicts a 20 stone, Jobcentre worker stretched over a tatty sofa, fetched $33.64m, far exceeding the previous record set in November by Jeff Koons' Hanging Heart sculpture that sold for $23.6 million.

The portrait was painted in 1995 by Freud, the 85-year-old grandson of the psychoanalyst Sigmund Freud, and is thought by some art experts to represent his best work from the 1990s.

The painting, which is part owned by Christie's, was sold by a private European collector.

The auctioneer declined to comment on the size of Christie's stake in the painting. A spokeswoman contacted during the auction also declined to name the buyer of the painting, who can decide at the end of the proceedings whether he chooses to be identified.

Referring to the woman Freud affectionately called "Big Sue", he has said that he was "very aware of all kinds of spectacular things to do with her size, like amazing craters and things one's never seen before".

After completing the painting 13 years ago, Freud gave Ms Tilley a print of her portrait which she later offered to bailiffs seeking to recover £700 of unpaid debt. They laughed at the offer and instead seized her electric kettle. The print was sold at auction in 2005 for £26,000. Ms Tilley posed for Freud for four years in the early Nineties and in most of his paintings of her he would cover her tattoos.

Christie's described Benefits Supervisor Sleeping as a "bold and imposing example of the stark power of Freud's realism. This picture is a simple and seemingly uncomposed depiction of one of the key features of Freud's art: the forceful and undeniable physical presence of people and things."

The sale price of the painting also beats the previous auction record for a Freud work of $19.3 million when IB and Her Husband (1992) went under the hammer in November last year.

The artist, whose sitters have included the model Kate Moss, said: "I paint people not because of what they are like, not exactly in spite of what they are like, but how they happen to be."

Art auctions conducted by Christie's and Sotheby's are being followed keenly by those outside the art world to monitor whether the credit crisis that has brought down one Wall Street bank and threatens to plunge America into a recession, is spreading to other parts of the economy.

Last night's auction represents just part of the Modern and Impressionist art auctions held in New York every spring by Christie's and Sotheby's. Tonight, Sotheby's is to auction a Francis Bacon triptych painted in 1976 which is expected to fetch about $70 million. At the same auction, Mark Rothko's 1956 Orange, Red, Yellow will also come under the hammer and is thought to be worth more than $35 million.

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