President Nixon's first reaction to the publication was that, since the study embarrassed the Johnson and Kennedy administrations rather than his, he should do nothing. However, Henry Kissinger convinced the president that not opposing the publication set a negative precedent for future secrets. The administration argued Ellsberg and Russo were guilty of a felony under the Espionage Act of 1917, because they had no authority to publish classified documents. After failing to persuade the Times to voluntarily cease publication on June 14, Attorney General John N. Mitchell and Nixon obtained a federal court injunction forcing the Times to cease publication after three articles. -- Wikipedia
Nixon probably had it right to begin with.
When you take into account how dogged and how devious he was about things, he probably should have just let it go.