The answer to this question depends on the context in which it is being asked. From one point of view, the statement is TRUE because the Constitution has always limited presidential power, both before and after the 1930s. For example, Congressional power to override a presidential veto has been in place since 1789, when the first government under the Constitution assumed office.
However, the question is FALSE to the extent that it implies the President obtained unlimited powers during or after the 1930s. As mentioned, the President has always had limited powers, from 1789 until the present day. Also, the only Constitutional amendments during the 1930s (20th [presidential succession] and 21st [repealing prohibition]) did not increase or decrease Executive power.