In the era since since there were 48 states (1913) and 50 states (1959) and since, there have been several Congresses in which either the US House of Representatives or the US Senate have had razor thin margins in membership, similar to what is happening in the 117th Congress, with a Democratic lead of only six seats in the House and an even split (50-50) in the Senate.
In the US House of Representatives, we have had close margins in the following 7 Congresses:
65th Congress 1917-1919 215-214 6 others
72nd Congress 1931-1933 218-216 1 other
78th Congress 1943-1945 222-209 4 others
83rd Congress 1953-1955 221-213 1 other
106th Congress 1999-2001 223-211 1 other
107th Congress 2001-2003 221-212 2 others
117th Congress 2021-2023 222-212 1 vacancy
In the US Senate, we have had close margins in the following 11 Congresses:
66th Congress 1919-1921 49-47
70th Congress 1927-1929 48-46 1 other, 1 vacancy
72nd Congress 1931-1933 48-47 1 other
82nd Congress 1951-1953 49-47
83rd Congress 1953-1955 48-47 1 other
84th Congress 1955-1957 48-47 1 other
85th Congress 1957-1959 49-47
107th Congress 2001-2003 50-49 1 other
108th Congress 2003-2005 51-48 1 other
110th Congress 2007-2009 49-49 2 other
117th Congress 2021-2023 50-48 2 other
Notice that both houses of Congress have had tight margins in the 72nd Congress (1931-1933); the 83rd Congress (1953-1955); the 107th Congress (2001-2003); and the present 117th Congress (2021-2023)!
These elections occurred at the time of the worsening of the Great Depression; the beginning of the Eisenhower Administration; the time of the contentious Presidential Election of 2000; and the time of the controversial Presidential Election of 2020!
The decades of the 1950s and the 2000s saw the largest number of tenuous majorities, with four Congresses in the 1950s and three Congresses in the 2000s having such results!
A total of 14 Congresses have had at least one house with a tenuous margin!
Whether the present tenuous majorities in both houses of Congress will continue in 2022 and beyond is the big question!