The opposition Nixon was truly worried about was the China Lobby, who determined US foreign policy for a couple of decades. But by 1972, the China Lobby seems to have been spent.
There was certainly opposition from conservatives, which is why it took Nixon to go to China to begin with. But their voices were drowned out in the applause.
From MacMillan, Margaret. 2007. Nixon and Mao: The Week that Changed the World. New York: Random House.’
p. 297
[Taiwan] had counted, too, on the ability of the of the China lobby to keep American governments in line. They had failed to see that it was slowly fading away, although they should perhaps have taken notice when its chief organizer abruptly resigned in 1969 and moved to London to start producing plays and when the New York Times referred to the “once powerful China Lobby.”
p. 321–322.
At 98 percent, Nixon’s trip to China registered the highest public awareness of any event in the Gallup poll’s history. The right wing fulminated to little apparent effect. A furious Buchanan threatened to resign from the White House staff on the grounds that the United States had made a deal with a Communist regime and sold out its ally Taiwan, but in the end he did not carry out his threat. The conservative journalist William F. Buckley Jr., who had been brought along on the trip in an attempt to win him over, publicly condemned the Shanghai communiqué and went off to support John Ashbrook of Ohio, a little-known Republican congressman who was trying to stop Nixon’s reelection.