Samardzija struck out nine and gave up one run on six hits and three walks over five innings, but was pulled after 97 pitches. He didn't have an easy inning and left with the score tied at 1 after the two teams exchanged home runs.
No one on the Cubs wants to see Dempster or Garza go, but everyone is aware of the rumors.
"Not knowing what's going to happen, you have to stay on your toes and understand tomorrow might be a little different," Samardzija said. "I understand what my role is on this team and what it's going to be in the future. I'm trying to do everything I can today, so down the road, when you are relied upon, you're ready to take the reins and do what you've got to do.
"Obviously, I want to be the guy, but it also would help to have Garza and Dempster throwing in front of you or behind you. ... We have a good competition with each other, we expect a lot out of each other and we'll keep going until we're told something different."
Cubs pitchers have helped, as they've compiled a 2.39 ERA in the last seven games, including a 2.81 mark by the starters.
Starlin Castro hit a game-tying solo home run in the fourth and Geovany Soto smacked a tie-breaking RBI single in a four-run seventh to spark the Cubs, who picked up their 13th win in the last 18 games.
"I think everyone's doing their part," Samardzija said of the recent success. "It's just kind of what we expected from ourselves from Day 1. We obviously went through a rut where we weren't playing good baseball. We've known we could play like this for a long time. It's just about being consistent and showing up every day and doing your job."
Wednesday's game was stopped with one out in the eighth because of rain, and called after a delay of one hour and 17 minutes.
"We'd have had to waste another hour and a half, two hours," Marlins manager Ozzie Guillen said. "The umpires said, 'We're not going to wait that long.' ... I think they did what they had to do. Unfortunately, we were down on the scoreboard."
With the score tied at 1 in the Chicago seventh, Alfonso Soriano singled, beating a throw from second baseman Omar Infante, and advanced on a wild pitch and a groundout by Bryan LaHair. Soto then lined a single to left that bounced over third baseman Hanley Ramirez. It was Soto's sixth hit in 36 at-bats with runners in scoring position.
"Hopefully that snowballs into swinging the bat a lot better with men in scoring position," Sveum said of Soto.
Darwin Barney then singled to chase starter Josh Johnson (5-7), and Luis Valbuena greeted Mike Dunn with a single to load the bases. Pinch-hitter Jeff Baker lined a double down the left-field line to drive in two, and David DeJesus added a sacrifice fly.
James Russell (3-0) picked up the win in relief of Samardzija, who was pleased with himself for not letting the game get out of control.
"The Marlins make me throw a lot of pitches every time I face them," said Samardzija, who lost in Miami on April 19. "Kudos to the top of that lineup. When you put [Emilio] Bonifacio and [Jose] Reyes back to back, as a pitcher, you really have to make sure you keep those guys off the bases. Not only are you trying to get good hitters out like Carlos Lee and Hanley and those guys, but you're also worrying about the guy on first base."
Reyes led off the Marlins' third with his fourth homer, but Castro tied the game with a leadoff blast of his own in the Chicago fourth, his eighth of the season.
Samardzija was able to limit the damage. The Marlins had a runner at third with two outs in the third, but he struck out Greg Dobbs. Bonifacio tripled to open the Marlins' fifth, but also was stranded as Samardzija got the groundouts when he needed them.
"He wasn't as efficient -- first-pitch strikes were tough," Sveum said "His split was OK, but it was a little bit short and bouncing and getting too far in front of home plate. Outs were a little tough for him, but he battled and did a great job and got the outs when he had to in the fifth."
The Marlins had an extra out in the fifth as Soto committed an error on a rundown, but again, Samardzija didn't flinch.
"After that rundown, I took a second," Samardzija said. "That's what I was happy about -- just taking my time and not rushing and making pitches I need to make and understanding there was still a chance to get out of it. Things like that, you learn from it."
And it should help him become a top-line pitcher.