Short answer is the US was in favor of recognizing the PRC as the "one China" and had assurances from Mao Zedong and Zhou Enlai that while the PRC would always pursue a "one China" policy, there would be no hard timetable or force to reunify.

George H.W. Bush, then UN ambassador, proposed a resolution whereby PRC would have a Security Council Seat but ROC would still have an assembly seat. He voted for this and opposed of the complete shutout of the ROC, which was proposed by the Albanian ambassador. [source]

The Nixon administration was very much in favor of normalizing relationships with the PRC. After a border dispute at the Ussuri River in 1969 the administration became concerned that the Soviets would invade China, and that PRC could be more receptive to resuming formal diplomatic relationships.

After several years of clandestine meetings between Henry Kissinger and Zhou Enlai - and ping-pong diplomacy, the two countries more or less agreed to disagree about Taiwan. [source: On China, Henry Kissinger, 2011]

I'm speculating, but I think normalizing relationships with the PRC was so important to the Nixon administration that anything short of a forced reunification of ROC was an acceptable cost to achieve that.