If I'm not mistaken, the Republican proposals (of this year) go that deep, at least for broad enough areas like "Labor-HHS-Education". I'm curious if there's any historical shade of plausibility for cuts this substantial. As I suspect the answer is "no", let me ask alternatively: what's the largest budget cut the US has seen in the past?
Question: Has the US government ever managed to cut 30% of its budget?
Across the board, in one year? yes in both 1945 and 1946.
According to Federal Budget Receipts and Outlays
In 1945 the federal budget was $ 92.7 billion dollars, In 1946 the federal budget was cut to $ 55.2 Billion. This amounts to a 40% cut.
Again in In 1947 it was further cut to 34.5 Billion, a 37% cut from the previously mentioned budget from 1946.
Generally the way the U.S. has successfully managed it's debt is not by massively cutting federal spending. Generally spending is held steady, or very modest cuts are made, and economic growth transform the deficit into a revenue surplus over time.
Truman reduced the deficit or increased the budget surplus in 1947, 1950, and 1953. with modest spending cuts. In 47 he tripled the budget surplus.
Eisenhower turned deficit spending into a budget surplus in 1955, 1959 by modestly increasing spending.
LBJ likewise transformed a significant deficit in 1968 into a small surplus in 1969 by modestly increasing spending.
Bill Clinton modestly increased federal spending every year in office, while transforming a 203 billion dollar deficit into multi year surpluses (1998-2001).
President Obama cut the deficit in half over his 8 years in office mostly by holding federal spending relatively constant.
You see if the budget is cut too fast the economy (GDP growth) is hurt. Shrinking GDP compounds the overall effect of the debt. So it's better to address debt by measures which impact deficits, with slower modest changes. Holding spending relatively constant and growing the GDP and tax base, shrinking deficits and reducing the impact of debt.