"in part" is a phrase of the word part. It means "to a certain extent." So, yes, it is used correctly in the sentence.

Let’s shorten your sentence as follows. “Our staggering national debt is due in large part to highly educated politicians and government officials.” The phrase "due in" is used “to attribute or assign a significant portion of a particular outcome or result to a specific factor.” So, "due in large part to highly educated politicians and government officials" suggests that a significant contributing factor to the large national debt is the influence of them. Here are two example sentences with the explanation. The increase in pollution levels is due in large part to the rapid industrialization of the region. (Explanation) Here, "due in large part to" is used to point out that a substantial factor contributing to the rise in pollution levels is the quick pace of industrial development in the area. His improved health condition is due in large part to his commitment to regular exercise and a balanced diet. (Explanation) In this sentence, "due in large part to" suggests that a significant factor in his improved health condition is his dedication to maintaining a routine of regular exercise and a balanced diet.