Almost certainly as much if not more so, because the most likely avenue to a public option would be to mimic TRICARE. In other words, public in name only because it would be the issuance of federal contracts to private insurers for administering "universal" coverage. And it's a virtual guarantee if legislation ever got that far, any sort of realistic or effective cost controls, regulations, or profit margin caps would be negotiated away in essence creating an unlimited pork mountain for private insurers.
The necessary factor in creating a public option that would be effective and provide cost control, at least in the US context of health care, would be to create a federal GSE, federally-owned corporation, or set of state-level health care cooperatives. TVA could be a model for health care administration in the US, for example.