The best known and perhaps most important constitutional amendment that is currently being proposed by one or more members of Congress is the balanced budget amendment. This is an amendment that is supported mainly by Republican members of Congress. A full discussion of the proposed amendment can be found here.
As its name implies, the point of this amendment would be to require the federal government to balance its budget every year. The amendment would do other things as well, such as a three-fifths majority of both houses of Congress in order to raise the statutory debt limit. However, its main provision would be to force the government to balance its budget.