How did presidential policy and supreme court decisions in the mid twentieth century United States contribute to a more involved national government?
This might be a topic suited for a large volume of American History. There might have to be some level of qualification about the term "mid twentieth century." In my mind, I would suggest that the nation which emerged from the Second World War had come to identify national identity with an involved national government. In staring down the threats of the Axis powers, national government led the way and created the path to help rid the world of fascism. From this, Americans were able to sense that national government's identity is not something from which aversion and evasion is needed. An example of this would be the case of the United States v. Darby, where the Supreme Court struck down the issue of child labor, emboldening business fair practices legislation as passed by Congress. Similar federal leadership as represented through the Supreme Court would have to be evident in the Brown vs. Board of Education decision. The notion of integrating public facilities "with all deliberate speed" was a federal mandate, and one where the federal government was more involved. It is no accident that President Kennedy was adamant about sending troops to escort students into the University of Alabama, a moment where the nation's attention saw the federal government providing both moral and political leadership. The same sentiment was felt when the political equivalent to this judicial sentiment was echoed in President Johnson's Civil Rights Act legislation in 1965. In both Darby Lumber and Brown v. Board of Education, the Supreme Court emboldened the federal government to become involved in the affairs of its citizens, helping the perception of government to be an institution to support the body politic's hopes of achieving the freedoms listed in the Constitution.
I agree with the above answer, and I would emphasize that you need to define "mid-century."
To me, the rise in the power of the national government can't be discussed without linking it back to the Depression and WWII. Both of those, more than anything after, led to an increase in the power of the central government. As far as the Supreme Court goes, before Darby, there was the "switch in time that saved nine" where the Court started allowing New Deal programs to stand after it had been striking them down (this is West Coast Hotel v. Parrish).
After WWII, the federal government continued to do more or less whatever it wanted up until the Reagan years. Even Republicans like Eisenhower and Nixon did a lot of things that increased and/or used the power of the federal government (building the interstates, aid to education after Sputnik, wage and price controls under Nixon).
So I would say that the Depression and WWII set a precedent and the need for the federal government to fight the Cold War added to that precedent. People got so used to the federal government acting that they went along with it until the '80s.
Starting with President Harry S.Truman he involved our nation in the Cold War,by fighting the spread of Communism in foreign lands and in this country.Although McCarthyism went to the extreme,it was connected to this naional watchdog effort.Truman was also noted for desegregating the armed forces during his tour in office.The 1954 Supreme Court Case of Brown vs Board of Education (Topeka Kansas) was certainly a landmark case.As a result ,efforts to desegregate places like Little Rock,Arkansas,Ole Miss was led by executive action.President Johnson's anti-poverty programs,like Head Start had a national impact.The introdution of Medicare,special education programs,and the G.I Bill after World War II also came during this time. The Supreme Court struck down all miscegenation laws with the Loving vs Virgina,1967 case, and the rights of the accused was extended in the Miranda vs Arizona ,1966 case.