Rep. Adam Smith (D-Wash.) made the remarks during an appearance at the Council on Foreign Relations on Thursday.
President Obama defended American exceptionalism Tuesday at the United Nations.
Kissinger said he remains optimistic that the deal would have a positive impact on the region and the world.
"President Putin and his associates do not believe in these values," McCain writes.
As recently as 2006, nearly three-quarters of Americans -- 73 percent -- saw Russia as an ally.
"I think there's probably some ... in all honesty that (oppose it) just because they dislike President Obama," McCain said.
The news was first reported by Foreign Policy, which (somewhat unwittingly) facilitated the agreement.
105 current members of Congress voted in favor of the Syria Accountability Act but now oppose or are leaning against authorizing military force.
"And he’s a little guy, but boy I tell you, he put me down in a millisecond," says Rep. Dana Rohrabacher (R-Calif.).
The White House has said it was the use of force that led to diplomacy.