The thing about that is Nixon was an extremely bitter, arguably paranoid person. Over the years between his vice presidency and presidency, he grew increasingly secretive. He was a person who wanted to win the presidency by the widest margin in history and wanted to be remembered among the likes of Washington and Lincoln. Any tie to the break-in would surely damage his reputation and he did not want to risk that. That's where the cover-up comes in.

He probably couldn't take the risk that Hunt and Liddy would sing while they were in prison. They'd been working for him a long time and knew too much. Watergate might just have been the tip of the iceberg. Besides, as they were official employees of Nixon's reelection campaign, he couldn't exactly just wash his hands of them. See White House Plumbers for more information.

In addition to what everyone else has mentioned, I personally subscribe to the view that Chris Matthews puts forward in his book Kennedy & Nixon. John Kennedy and Richard Nixon had a long friendship-their offices were across the hall, after surgery at least once, Nixon sent a get-well card to Jack, etc.

Long story short, in the 1960 election, Nixon felt he had been cheated out of victory: JFK was in his eyes a womanizer and addict who was unfit to be President and there are arguments that he didn't take him very seriously. However, the first debate changed this around and ended with what is generally considered a decisive victory for Kennedy-Nixon followed in his footsteps and let him set the tone of the argument. Ike Eisenhower, who Dick Nixon had served as VP during both terms, did not stump for Nixon the way he should have, limiting his support on this front.

He lost the election and spent the rest of his life feeling that he'd been cheated. When RFK ran for President, Nixon feared that he would have to go up against the ghost of JFK, which was a realistic fear: RFK relied heavily on his deceased brother's imagery in order to further his campaign. However, his Presidential campaign was brought to a premature ending by an assassination, but the Kennedy dream stayed alive, passing down to Ted Kennedy (arguably).

The argument proposed by Matthews is that, in 1972, Nixon feared a Kennedy revival and having to run against Ted Kennedy (in spite of him being stuck with the albatross of Chappaquiddick around his neck) and his fear of this Kennedy restoration, and a desire to avert, led to his involvement and attempted coverup of the Watergate affair.

Sources:

Christpher Matthews, Kennedy & Nixon, the Rivalry that Shaped Post-War America

Michael O'Brien, John F. Kennedy

Conrad Black, Richard M. Nixon