Wherry was born in Liberty, Nebraska, to David Emery and Jessie (née Comstock) Wherry. He received his early education at public schools in Pawnee City, and graduated from the University of Nebraska in Lincoln (where he was a member of Beta Theta Pi fraternity) in 1914. From 1915 to 1916, he studied business administration at Harvard Business School. During World War I, he served in the U.S. Navy Flying Corps (1917–18).

Wherry entered politics as a member of Pawnee City’s city council, serving in 1927 and 1929. He was the mayor from 1929 to 1931, simultaneously serving as a member of the state senate from 1929 to 1932. Wherry was an unsuccessful candidate for the Republican nomination for governor in 1932 and for U.S. Senator in 1934.

In 1938, Wherry was again elected mayor of Pawnee City, serving until he left for Washington and the U.S. Senate. He was chairman of the Nebraska Republican Party from 1939 to 1942, and Western Director for the Republican National Committee from 1941 to 1942.

In 1942, Wherry was elected to the U.S. Senate, unseating incumbent George W. Norris. He was reelected in 1948 and served until his death. He served as Republican whip from 1944 to 1949 and minority leader from 1949 to 1951. He was also one of the few postwar politicos to see the plight of the defeated Germans. “The American people should know once and for all that as a result of this government’s official policy they are being made…accomplices in the crime of mass starvation…Germany is the only nation subjected to a deliberate starvation policy…”

In 1945, Wherry was among the seven senators who opposed full U.S. entry into the United Nations.

On April 11, 1945, US forces liberated the Buchenwald concentration camp, which was established in 1937 and caused the deaths of at least 56,545 people. General Eisenhower left rotting corpses unburied so a visiting group of U.S. legislators could truly understand the horror of the atrocities. This group was visiting Buchenwald to inspect the camp and learn firsthand about the enormity of the Nazi Final Solution and treatment of other prisoners. Wherry visited the camp along with Alben W. Barkley, Ed Izac, John M. Vorys, Dewey Short, C. Wayland Brooks, General Omar N. Bradley, and journalists Joseph Pulitzer, Norman Chandler, William I. Nichols and Julius Ochs Adler..

Whatever the issue, he could be counted on as a strong opponent of the presidency of Harry Truman. Wherry was the unsuccessful leader in the fight to block the Marshall Plan in Congress in early 1948. Congress, under the control of conservative Republicans, agreed to the program itself and the funding for multiple reasons. The 20-member conservative isolationist wing of the party was led by Wherry. He was outmaneuvered by the internationalist wing, led by Senator Arthur H. Vandenberg. Wherry and his men argued that it would be “a wasteful “operation rat-hole”; that it made no sense to oppose communism by supporting the socialist governments in Western Europe; and that American goods would reach Russia and increase its war potential. Vandenberg admitted there was no certainty that the plan would succeed, but said it would halt economic chaos, sustain Western civilization, and stop further Soviet expansion.

Senator Robert A. Taft, the most prominent conservative, hedged on the issue. He said it was without economic justification; however it was “absolutely necessary” in “the world battle against communism.” In the end only 17 senators voted against it on March 13, 1948.

Wherry was openly opposed to homosexuals, telling Max Lerner in a 1950 interview that “You can’t hardly separate homosexuals from subversives” and “But look Lerner, we’re both Americans, aren’t we? I say, let’s get these fellows [closeted gay men in government positions] out of the government.” He also publicized the fear that Adolf Hitler had given Joseph Stalin a list of closeted homosexuals which he believed Stalin would use to blackmail them into becoming Soviet spies. In the spring of 1950, Wherry joined Senator Lister Hill, a Democrat from Alabama, in a Congressional investigation of homosexuals in government, particularly the Department of State. He was particularly concerned with communist influence, saying “Only the most naïve could believe that the Communists’ fifth column in the United States would neglect to propagate and use homosexuals to gain their treacherous ends.”

Wherry died in Washington in 1951 at age 59, while serving as Republican Floor Leader. Recovering from abdominal surgery a few weeks earlier, he felt ill and was admitted to George Washington University Hospital and died of pneumonia several hours later.