Following systematically the generalized Hamiltonian approach of Batalin, Fradkin and Tyutin, we embed the second-class non-Abelian SU(2) Higgs model in the unitary gauge into a gauge invariant theory. The strongly involutive Hamiltonian and constraints are obtained as an infinite power series in the auxiliary fields. Furthermore, comparing these results with those obtained from the gauged second-class Lagrangian, we arrive at a simple interpretation for the first-class Hamiltonian, constraints and observables.