Without defending the constitutionality of the line-item veto statute struck down by the Supreme Court, I’d point out that impoundment wasn’t unique to Richard Nixon — it actually began at least in 1801. Every president from Thomas Jefferson to Nixon was thought to have impoundment power. Nixon went much further in impounding spending than any of his predecessors, however, and had some other, uh, problems going on at the time.
Even then, Congress didn’t appeal to the Constitution or run to the courts to stop Nixon’s impoundment. Instead, they passed a statute, the Congressional Budget and Impoundment Control Act of 1974, getting rid of the practice. Under the law, the president retains the power to propose recission of certain items, though that falls short either of the line-item veto or the enhanced recission authority pursued by the Bush administration.