Does Jeff Samardzija need a wake-up call?

The Cubs saw why their No. 1 starter could be heading toward a megadeal during Monday night’s two-hit shutout, hitting 96, 97 and 98 mph in the ninth inning. Samardzija loved beating the White Sox – a team he grew up rooting for – at U.S. Cellular Field, not far from his family’s home base in northwest Indiana.

After a 7-0 victory, the former Notre Dame All-American wide receiver said he’s always felt comfortable in pressure situations and then admitted “sometimes you can lull me to sleep” with other games that aren’t as important.

“I don’t know if that’s a maturing process,” manager Dale Sveum said Tuesday on the South Side. “Sometimes that’s what this game can do to you. You figure it out. You just have to do something different to make yourself in that same atmosphere all the time.”

Sveum thinks Samardzija profiles like a big-game pitcher, and not just because he was once a football star, though the experience of playing in front of 100,000 fans and national television audiences certainly helped.

Sveum pointed to two performances against the Pittsburgh Pirates at PNC Park: eight scoreless innings on Opening Day; and the complete game on Sept. 8 last year when Samardzija knew it was his final start before getting shutdown.

“He went out and blew it all out,” Sveum said, “but sometimes that arm just ain’t quite the same every time.”

Sveum made a comparison to Yovani Gallardo, the All-Star pitcher he got to know as a Milwaukee Brewers coach. Sveum felt Gallardo could at times drift from start to start but always showed up for the big games.

“That’s what you got to be weary of sometimes, but (Samardzija) is such a strong guy with a mentality,” Sveum said. “He keeps himself in phenomenal shape to go nine innings and to have that kind of power throughout a game.”

Something’s clicked for Samardzija (3-6, 2.85 ERA) across his last three starts. He’s given up only three runs in 24 innings, notching 23 strikeouts against five walks, a transformation for someone who in recent years had existed at the fringes of the roster and struggled in shifting between the bullpen and the rotation.