Some of the Contract had to do with the way the Congress operates: for example, term limits for committee chairs, requiring all laws that apply to the rest of the country apply to Congress, banning proxy votes. Each of these has to be enacted by each house of Congress to apply to itself. Since each house determines its own rules for procedure, the House of Representatives can term limit its own committee chairs but not those of the Senate, and vice versa. I believe most of these were passed for the House of Representatives, which was the driving force behind the Contract. The Senate balked because they didn't feel obligated to the Contract in the way the House did. There was one requiring a 2/3 majority for a tax increase, and I don't think that passed, and it is probably unconstitutional. The first proposal, that Congress should have to obey laws passed for others, was very sensible and popular but some Republican Congressmen immediately tried to make exceptions. The Congressional reforms were probably the most popular part of the Contract. I don't think the Democrats are obligated to keep them now that they control the House.
The other provisions would have been actual laws, and the promise was to bring them to the floor, not necessarily to pass them. One of them, to limit Senators and Representatives to terms adding up to not more than 12 years, required an constitutional amendment, which needs a 2/3 vote in each house and the approval of 3/4s of the states, and the bill didn't even pass the House. Some congressmen made term-limit pledges. Some of them honored their pledge, like Tom Coburn (who came back a few years later as a Senator), and others, like my own Congressman, violated their pledges. In any case, once the Republicans took over, most of them conveniently forgot about term limits, and since a constitutional amendment was not about to pass (the Democrats were against it and thr Republicans didn't have a very large it became a dead issue. The whole term-limits affair made a lot of people question the sincerity of the Republicans. After all, if you want term limits, why not stop running for office?
Where the Contract ran into trouble was with things such as Social Security, a particular welfare reform which was passed by Congress and vetoed by President Clinton (an alternative was later passed), a balanced budget amendment (failed in the Senate--and what would Bush do with that?). Two tort reform bills passed Congress and were vetoed by Clinton. One of the vetoes was sustained and the other overridden.