Actually, I agree with you. History has shown that the American public opinion turns anti-war in prolonged military campaigns.
The thing is, the Americans know that. When they respond it will be a Gulf War 1 style campaign with a huge coalition and overwhelming firepower. Even if the Americans suffer a initial Pearl Harbor type defeat, they will still keep coming and their next attack would be with full force of her allies. This attack will be massive and would aim to destroy the PLA as a fighting force and to cripple the Chinese economic infrastructure. Also, NATO doesn't have to wage a ground war, their main objective would be to destroy the PLAN and the PLAAF. The NATO countries still have a respectable navy and air force. Also, IMHO, the Americans have a -huge- technological advantage vis-a-vis any major military power.
Also, historically, American attrition has mainly occurred -during- an occupation of a hostile territory, not during their main "Army vs. Army" campaign. They know that occupying Chinese soil would be horrendously expensive. They would just be content to destroy the Chinese forces in theatre and wrangle heavy diplomatic concessions. The Americans are the best at conventional military campaigns and the Chinese cannot back down from one. The political costs of retreating would be too high for the Politburo [The "saving face" concept].
The Americans have to let the Chinese "wither-on-the-vine". They have to cut their Oil, mineral shipments and their export markets.
The Americans are also the bet in the world at building weapons, and building them fast. Even if the fastest manufacturer of weapons wins this war, it will be the Americans.
Now, with regards to the logistics issue, the Americans have a huge enough fleet to keep their forces supplied indefinitely, especially with no Chinese submarine threat and proximity of the Area of Operations to Australia, Taiwan, Japan, South Korea, India [to an extent] and the Philippines.
They did overcome these hurdles while fighting in Germany, Japan, Korea, Vietnam, Iraq and Afghanistan. It won't be easy, but it will definitely be done.
Lastly, I am taking this in from the American POV. There is a definite bias here, I admit.