The jokes started after Paisley feigned back pain.
"Hey, do you have that Obamacare?" Underwood asked, drawing raucous laughter and applause from the audience. "I started signing up last Thursday and I'm almost done."
After retrieving a laptop, Paisley and Underwood poked fun at HealthCare.gov's woes.
"Why is it spinning?" asked Paisley, pointing at the screen.
"Oh, it does that," Underwood said.
"Why is it smoking?" Paisley then asked.
The two eventually broke into a rendition of George Strait's classic "Amarillo by Morning."
"Obamacare by morning," they sang. "Why's this taking so long?"