There was already a huge loss of face involved - the US losing to little Vietnam, and the whole dominoes argument used for years. I don't think the opposition to the war did much to influence those already committed to it, they could be dismissed as radicals, leftists, soldiers against it as miguided, etc.

As Chomsky said, it was really the change in elite opinion that counted:

Clifford, like McNamara, had to deal with frequent requests for additional troops from military commanders in Vietnam. When he became secretary, the authorized force in Vietnam was 525,000. Soon after moving into his Pentagon office, Clifford persuaded Johnson to deny General William Westmoreland's request for an additional 206,000 American troops in Vietnam.

...
Eventually Clifford moved very close, with Johnson's tacit support, to the views McNamara held on Vietnam just before he left office -- no further increases in U.S. troop levels, support for the bombing halt, and gradual disengagement from the conflict. By this time Clifford clearly disagreed with Secretary of State Dean Rusk, who believed, according to The Washington Post, "that the war was being won by the allies" and that it "would be won if America had the will to win it." After he left office, Clifford, in the July 1969 issue of Foreign Affairs, made his views very clear: "Nothing we might do could be so beneficial . . . as to begin to withdraw our combat troops. Moreover . . . we cannot realistically expect to achieve anything more through our military force, and the time has come to begin to disengage. That was my final conclusion as I left the Pentagon...."

http://en.wikipedia.org/wiki/Clark_Clifford

Maybe it's because I'm a Londoner - that I moved to Nice.