They were planning to do a lot more than spy, too. They were planning to kill both Daniel Ellsberg (if they couldn't discredit him first, e.g. by giving him LSD to make him nonsensical just before making a public appearance) and the journalist Jack Anderson.
Classy. Though considering how it was recently revealed that Nixon intentionally torpedoed the talks with Vietnam before he got elected, that's totally in line with the character.