A lot of folks on FR like to laugh about China's military capabilities, but I'd sure hate to be on the first naval strike force that has to penetrate their air cover. China has between 850 and 1200 front-line fighter-bombers and another 1500 to 1800 older models. Even if they only send one-quarter of these aircraft at one of our carriers, let's look at the numbers. They could send in four hundred older aircraft, followed by two hundred fifty newer models. An American carrier can send up approx. 48 fighters and fighter-bombers to engage these attacking aircraft. If all 48 American aircraft are carrying eight missiles, that means that there are 384 available AAM's. Let's say that the American fighters achieve a 75% kill rate, this means that they have downed 288 enemy aircraft, which means that there are one hundred twelve older model Chinese fighters heading in, followed by the two hundred fifty newer models. The SAM's on the escorting cruisers and destroyers would now engage the enemy aircraft, but most carrier task force's only have one cruiser and two destroyers along as escort. A Ticonderoga-class cruiser can carry 122 SAM's and an Arleigh Burke-class destroyer carries 96 SAM's. This means that there are 314 SAM's on these three ships. Going with the same 75% kill rate as the AAM's, they would only down 235 enemy aircraft, meaning that one hundred twenty-seven enemy aircraft, most likely their most modern models, would blast through the fighter and SAM screen. These fighter-bombers can carry an average of two anti-ship missiles each, meaning that two hundred fifty-four ASM's would be screaming into the American fleet, which would ruin everyone's day.
In an all-out war with the Chinese we would have established bomber bases out in the Pacific to knock out their bases and prevent this scenario from occurring, but if an American carrier force is heading in to support Taiwan from a bunch of Chinese saber rattling and China launches an aerial blitz, they could easily overwhelm one, maybe even two carrier battle groups with their aerial assets, not to mention their submarines.
I believe that the US would be able to defeat the Chinese in a modern conventional war, but it will not be pretty and it will be very bloody and very prolonged.