And with the Sharks' lack of postseason success in recent years, Thornton has received much of the blame.
Fair or not, the superstar has acquired a reputation for burning brightly in the regular season and flaming out during the Stanley Cup Playoffs. The 30-year-old playmaker has amassed 931 points in 915 regular-season games, but just 53 points in 75 postseason contests.
If the Sharks want to exorcise their playoff demons this spring, Thornton will need to raise his game.
And he's well aware of that.
"It's normal to have pressure on your best players," Thornton said. "It's normal when your team's not going good that your leaders have to step up.
"That's just the nature of the beast. You go to any city, that's the way it is. It doesn't matter if you're in the hunt for a playoff spot or in the playoffs, your best players have to be your best players at crunch time."
San Jose hasn't moved past the second round since Thornton's arrival in 2005-06. In the previous three seasons, the Sharks have finished first in the Western Conference twice and second the other time.
This season, the Sharks finished first in the West again, edging Chicago by one point.
During those previous early exits, Thornton has 4 goals and 22 assists in 30 games. Not terrible by any stretch of the imagination, but the Sharks will need more from their star if they want to win a Stanley Cup.
And, Thornton has had another fine regular season. He finished with a team-high 89 points in 79 games, and his 69 assists are his highest since he had 92 during his Hart Trophy-winning season of 2006-07.
"It's normal to have pressure on your best players. It's normal when your team's not going good that your leaders have to step up." -- Joe Thornton
The Sharks were 2-1 in those three games, and at the very least, that little stretch could give the team some confidence that it can win without Thornton.
"Heading into the playoffs you have to have contributions from everybody," Sharks coach Todd McLellan said. "Teams will reel in on the top scorers, the top players on each team as they try to stay even, and try to stay ahead if they can. The third- and fourth-line players have to contribute."
It's one thing to win without Thornton in the regular season. But, if the Sharks want to go deep into the playoffs, they'll need their best player to play like it.
Follow Dave Lozo on Twitter at: @DLozoNHL