When the people swear to a new covenant in Nehemiah 10, they're recommitting themselves to the same values that they'd earlier failed to uphold. They agree to abide by the Law of Moses, to avoid marrying foreign women, to observe the Sabbath, and to fulfill their duties toward maintaining the Temple and the priests. It's not quite as ambitious as Isaiah's vision of a new covenant or Ezekiel's; there's no world of universal peace and love, free from death and violence. Rather, it's a fresh start—a chance to pick up the pieces and give it another shot.
The new covenant is also a symbol of their re-constituting themselves as a people, of reassuming their identity as one nation. This time, however, the people seem more competent. True, there's some backsliding, but the prophets and people like Ezra and Nehemiah seem fairly capable of handling it and setting things straight.