In the elections of 1994, part of the Republican platform was to pass legislation setting term limits in Congress. After winning the majority, they brought a constitutional amendment to the House floor.
It limited members of the Senate to two six-year terms and members of the House to six two-year terms. Because the Republicans held 230 seats in the House, they were able to get a simple majority.
However, constitutional amendments require a two-thirds majority, or 290 votes, and the votes to restrict term limits fell short of that number. In May of 1995, the U.S. Supreme Court ruled against term limits in Congress in the case of U.S. Term Limits v. Thornton. By a 5-4 vote, the justices found that states could not impose them on the U.S. Congress.