From the Contract With America, both, the Balanced Budget Amendment and Term Limits for Congress were voted on and failed to pass. Plus, all of the Contract With America items were profoundly watered down, before the final votes were taken.
This is what happens when you get your information from Michael Weiner, a former liberal loudmouth who became a nominally conservative loudmouth when it occurred to him that there was a larger radio audience on the right: You end up working with the partial knowledge Weiner needed to make his specious critique.
The Contract With America could not, and did not promise to pass anything. It could not because a large enough percentage of Republican incumbents refused to sign, because some of the bills in question were Constitutional Amendments (requiring a 2/3 majority plus ratification), and because Clinton retained his veto power (and used it).
Weiner is mostly likely obtaining his partial knowledge of this subject through libertarian websites.