I recently wrote about China's efforts to develop an "assassin's mace" to take out our carriers in the event of a war (say,picking a country at random as an example, over Taiwan).
An issue separate from whether the Chinese can achieve this is whether it would matter if they did.
Sure, losing a carrier would be a huge prestige blow; but if we could withstand the propaganda impact, would losing a carrier or two stop us from successfully intervening over Taiwan and beating China? The bigger question is whether China could conquer Taiwan before we intervene. But in terms of the naval battle, I think we'd still wipe up the PLAN even without our carriers once we enter the battle.
As I argue in this post, it has been a long time since our carriers were our nearly sole offensive weapon. And carriers may even become a liability in time--a propaganda loss for losing one without a commensurate gain in capabilities for preserving them. In the 1970s, it made sense for the Soviets to target our carriers; but in the decades since then, anti-ship and land-attack missiles have spread to all of our surface combatants and submarines. And as we network what we have, the ability of our Navy to mass effect on the enemy has become independent of carriers.
I guess the main question then becomes, can we deploy sufficient fighter aircraft to help control the skies over Taiwan without carriers? If we can cover Taiwan from Guam and Okinawa and even get the Philippines to host an air expeditionary wing, we wouldn't need carriers for the fighter aircraft they carry any more than we need their strike aircraft to strike Chinese ships. If we can safely base aircraft on Taiwan the aerial refueling issue disappears--though defending against incoming guided ballistic missiles would be pretty tough, I think. I don't count on basing on Taiwan in the early stages, at least.
So, China could swing their magic mace and hit our war horse without harming our ability to actually fight and beat them with masses of missiles distributed across the western Pacific.
And the scary thing is, if the Chinese mistakenly think such a blow will win the war for them, war will seem very rational to them, and they will be more likely to swing the mace and go to war with us.