In The Great Gatsby, Tom and Daisy have little in common except each other and their way of life, daily routines, and the status quo they form. Daisy is, or at least would like to be, romantic, while Tom is wholly and proudly pragmatic. Daisy understands the predicament of a female living in a patriarchal society. Though she doesn't like it, she knows that the way for a woman to succeed is to be pretty and charming and, thus, stays with Tom. This is pragmatic, yes, but Daisy is pragmatic out of necessity. She also stays with Tom even when Gatsby tries to steal her away, because Gatsby asks "too much." The inference is that the romance between Gatsby and Daisy that took place years before meant more to Gatsby than it did to Daisy. Gatsby assumes that Daisy never loved Tom, but Daisy refuses to agree.
In some ways, the relationship between Tom and Daisy becomes more open by the close of the novel, but this is probably superficial. Tom probably won't take more notice of her and treat her well for very long.
On a fundamental personality level, Tom and Daisy do not seem to have much in common. Nick Carraway describes Daisy as vivacious and charming, while Tom comes across as haughty, serious, and somewhat stilted in his manner. Daisy laughs much more than he does. Throughout the novel, Tom hardly ever smiles or seems cheery. On the whole, then, it appears as if Daisy is much happier than her husband. This attitude, however, is part of the superficial image that she presents; she is just as cynical as her husband. For example, she tells Nick in Chapter 1:
“Well, I’ve had a very bad time, Nick, and I’m pretty cynical about everything.”
Tom's cynicism is evident in his remarks about civilization. He superciliously tells Nick:
“Civilization’s going to pieces.... I’ve gotten to be a terrible pessimist about things. Have you read ‘The Rise of the Colored Empires’ by this man Goddard?”
Tom and Daisy disguise their general pessimism by repeatedly indulging in mundane activities. Tom, for example, tells Nick about transforming a garage into a stable (instead of doing it the other way round). Daisy speaks of a butler's blue nose and, to sound appealing and intriguing, refers to the singing of a nightingale as romantic. The two go on trips to different places and spend time indulging their whims in New York. These purposeless activities are an indication of how bored and without vision they are. To illustrate, Nick makes the following apt observation about them:
They had spent a year in France for no particular reason, and then drifted here and there unrestfully wherever people played polo and were rich together.
Tom and Daisy are careless and superficial. Their friendships are shallow and lack real meaning. They tend to objectify people. Tom sees Myrtle as a plaything, while Daisy uses Jay Gatsby to get back at Tom for his indiscretions. She sees her daughter as something to be put on display. Both characters lack depth. They reveal their shallowness in how quickly they forget the objects of their so-called affection when these characters die.
Nick Carraway is disappointed and disgusted by them and includes them in "the rotten bunch" that he refers to when speaking to Jay. It is evident that Daisy's and Tom's actions and personalities are informed by their excessive wealth. They have too much of everything in material terms but lack true insight, love, or commitment.
Daisy and Tom stay together because, as far as Daisy is concerned, Tom provides her a life of comfort and luxury. She has the security of knowing that, in material terms, she will never be in need of anything. It is this materialism that makes it easy for her to eventually reject Jay by telling him that he "wants too much." She is not prepared to sacrifice the security of old money that Tom provides. Tom sees Daisy more as a trophy than anything else. She provides credibility to the image of a good husband and caregiver that he wants to project. He is the typical "family man." Being married to her provides the comfort that he has someone to turn to no matter what.
There is very little change in Tom and Daisy's relationship in the novel. The only real crisis they face is the one Jay Gatsby presents. Tom is disturbed by his wife's affair with Jay. In a show of unexpected sensitivity and affection, he almost pleads with her when confronted with the real possibility that he might lose her. Daisy, on the other hand, uses the affair to gain the upper hand on Tom, albeit for a brief moment. She never really intends to leave him and returns to him soon after she accidentally kills Myrtle Wilson. One might have expected her to turn to Gatsby. Instead, she leaves with Tom to some unknown destination soon after.
In the end, Tom and Daisy Buchanan revert to what they have always been: frigid, inconsiderate, materialistic, superficial, and disaffected. It is almost sure that their relationship will, in spite of the little hiccup, continue in the same manner because, after all, they don't really care.