According to The Space Shuttle Decision, the White House Office of Management & Budget, at the end of 1971, had concerns:
Similarly, the OMB would not permit its shuttle to be all things to all people; its memo to Nixon stated that "for national security purposes, we may not want all our eggs in one basket." The OMB stated explicitly that the nation was to "retain the reliable Titan III expendable booster to launch the few largest payloads that would not fit the smaller Shuttle. These include space telescopes and large intelligence satellites."
But at that time the shuttle configuration being considered had a 10x30 foot payload bay with 30,000 lb capacity, which wouldn't accommodate the largest spy sats, unlike the 15x60 bay and 55,000+ lb capacity of the actual shuttle.
I'm sure many people involved in the cost-benefit analysis of the shuttle program felt that the proposed flight rates were unlikely to be reached, in which case using existing launchers (Delta, Atlas, Titan) would have been more cost-effective for any mission not requiring crew, but I can't find any particular public statement arguing against the shuttle-only plan on that basis.