The Diet's movements turned into a political tug-of-war between the ruling and opposition parties over this issue.
Literal
Diet [attributive-の] movements [topic-は] this problem [concerning-をめぐる] ruling-opposition-party [between-間の] political tug-of-war [as-と]-became.
Political news. ~をめぐる ('concerning, surrounding') is the attributive of ~をめぐって — a formal pattern for an issue around which discussion/debate revolves. 綱引き ('tug-of-war') is used both literally and metaphorically for political/organizational struggles. 与野党間 ('between the ruling and opposition parties') combines 与党 + 野党 + 間 ('between').