While the Solid South was a dominant political phenomenon in the midcentury United States, it is not accurate to say that it was not so solid. The Democratic Party maintained a stronghold on the Southern states for decades, due to various factors such as the legacy of the Civil War and Reconstruction, racial issues, and the appeal of Democratic policies to the region's voters. However, there were certain pockets and exceptions within the Solid South where Republican candidates and ideas did make some inroads and challenges the Democratic dominance:

1. Republican Strongholds in the South:

- Some Southern states, such as Texas and Florida, had pockets of Republican support, especially in urban areas and among certain demographic groups.

- Certain congressional districts within Southern states occasionally elected Republican representatives.

2. Challenges to One-Party Rule:

- There were occasional challenges to the Democratic monopoly in Southern politics by third-party candidates or independent politicians who appealed to disaffected voters.

3. Shifts in Political Alignments:

- Over time, demographic shifts and changing socioeconomic conditions in the South began to erode the Democratic Party's dominance, leading to the rise of Republican strength in the region in later years.

4. Republican Gains in Presidential Elections:

- While the Solid South generally supported the Democratic candidates in presidential elections, there were instances where Republican presidential candidates made significant gains, such as Dwight Eisenhower in 1952 and 1956.

5. The Civil Rights Movement and Voter Suppression:

- The Civil Rights Movement of the 1950s and 1960s led to increased political activism among African American voters in the South, which challenged the existing political order and contributed to the gradual weakening of the Solid South.

- However, voter suppression tactics and other barriers prevented many African Americans from fully participating in the political process.

6. Emergence of Moderate Republicans:

- In some cases, moderate Republicans were able to appeal to Southern voters by focusing on economic and social issues rather than directly challenging racial issues.

In conclusion, while the Solid South was a powerful and enduring phenomenon, it was not completely impenetrable. There were pockets of Republican strength, occasional challenges to Democratic dominance, and shifts in political alignments that gradually weakened the solidity of the South in US politics.