With the Academy Award hullabaloo set to sweep Steven Spielberg's Lincoln into office come Oscar night, spare a thought for another great American president who has been given the big-screen treatment.

Opening in the US at the tail-end of last year, four weeks after Lincoln, was Hyde Park On Hudson, an intimate and charming portrait of Franklin D Roosevelt, directed by Englishman Roger Michell, starring Bill Murray and Laura Linney.

However, while Lincoln was lauded from the reviewers' rooftops, Hyde Park On Hudson received a critical kicking stateside and struggled to a measly $5 million at the US box office, compared to Lincoln's mighty $160 m. As a small-budget adaptation of writer Richard Nelson's BBC radio play (with an excellent Murray in his first lead since 2005's Broken Flowers), it was not meant to compete head-on with Spielberg's mega-money opus, yet its total neglect by American audiences is surprising and revealing.

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"No-one knew about Daisy," says Linney. "Very few people know about Daisy now even though the letters and diaries have been published. A lot of people knew about Lucy Mercer and the constellation of other women in his life and how his marriage worked, but not so much about Daisy. She never, ever spoke about her relationship with the president. No-one ever thought she would have much information to share because she was so modest, so much in the background, quiet, and she never called attention to herself and no-one ever called attention to her."

Some pages from Daisy's diaries were missing, but the letters and other writings reveal a rich and rather touching familiarity between a woman who called herself the "Little Mud Wren" and who saw herself as nothing more than "part of the furniture" around the president's home at Hyde Park On Hudson in the state of New York.

"Then when Daisy died at the age of 100," continues Linney, "and they found this suitcase of letters under her bed, it showed how intimate the two of them were, that it was a deep, deep friendship which probably had a sexual component to it at one point. But from the time that they met until the end of his life – and she was with him when he died – she was an important part of his support team."

Indeed, while the one firm sexual encounter in the movie, in Roosevelt's car, upset some American critics (it's not in the diaries, for a start), that aspect of the relationship is less important than the emotional. Murray, in fact, describes FDR and Daisy's fumbling as "kind of childlike" and "not what sex is to most people". He adds: "It's not what sex might be to one of us, but it's really an intimacy. And it's not like the guy is a stallion or anything. The guy is on crutches."

Hyde Park On Hudson is a film that plays with a hint of farce at times and reveals Roosevelt as an impish, dazzlingly bright and energetic man even though he is wheelchair-bound for most of the film, an after-effect of acute childhood polio. His battle against the disease is legendary and Murray captures that spark of vitality that drove him to such giddy heights, revealing also a fine sense of humour and willingness to look at his affliction with a wry eye. That said, being the president, he was sensitive about the manner in which he was portrayed in public. His strong relationship with the press ensured he was never photographed in the chair. In fact, the only photos that do survive of the president in his wheelchair were taken by Daisy.

"I don't think Daisy was even looking for it," adds Linney on the relationship. "I think there was someone who needed her and what she had to give. He got many different things from many different people, but from her I think he got that sense of being grounded and safe and he could relax, and not hold it all up. He could be a man in a wheelchair with her."

It was Daisy who gave Roosevelt his Scottish terrier, Fala, a dog that became so famous he had his own biography.

"Daisy called herself part of the furniture," Linney continues. "I knew that she was a photographer, and so was someone who looks and observes, and that was something that made her special, particularly in that world – she was not seeking any attention.

"What she received, what she shared and what she had, she didn't need to share with anybody. It didn't belong anywhere else. There was something about how rock-solid her character was. She was from the same place as him. They had grown up in the same area and he felt safe with her. He could say anything to her and knew that it would never go anywhere else."

In the modern-day world of the tabloid kiss-and-tell, Daisy comes across as something of a treasure and Linney gives a controlled, nuanced performance as a woman who must accept that the gift of her relationship comes with a price, as she learns that the man she loves is not necessarily everything that she thought he was.

Linney missed out on the award nominations for her performance in the film, which was not surprising given the antipathetic response from US cinemagoers, although she already has three Oscar nominations under her belt – twice in the best actress category (for You Can Count On Me and The Savages) and once as best supporting actress (Kinsey) – in a film career that's also taken in the likes of The Truman Show, Mystic River and The Squid and the Whale.

Her stage credits include The Seagull, Hedda Gabler and Uncle Vanya – as well as The Crucible, Sight Unseen and Time Stands Still, all of which earned her Tony Award nominations. She has picked up two Emmy Awards, one for her role in one of the adaptations of Armistead Maupin's Tales Of The City and for her recurring role as Dr Crane's love interest, Charlotte, in Frasier. Her current TV show, The Big C, earned Linney a second Golden Globe win in its debut season. Launched on America's Showtime channel in 2010, it is set to enter its fourth season in April (it's been shown on More4 in the UK). The series follows Linney's suburban wife and mother, who is diagnosed with melanoma and reappraises the relationships in her life.

"I have done a lot of television," she says, "but this show was a really challenging and worthwhile exploration of seeing how, when things are so overwhelming, painful and upside-down, comedy is the thing that people turn to as a life-preserver. It really explores how comedy can crystallise and bring a sense of truth to something instantly."

One suspects President Roosevelt might agree.

Hyde Park On Hudson is released on Friday.