Well-Structured pushdown systems (WSPDSs) combine pushdown systems and well-structured transition systems to allow locations and stack alphabets to be vectors, and thus they are unbounded. States change with the push and pop operations on the stack. The model has been said to be "very close to the border of undecidability". This paper proposes a general framework to get the lower bounds for coverability complexity of a model by adopting the reset-zero method. The paper proves that the complexity is Tower-hard when a WSPDS is restricted with three dimensional state vectors, and Hyper-Ackermann hard for the general WSPDSs.