Soriano went 1-for-3 in a rehab outing for Triple-A Iowa against Tucson and could be leading off on Wednesday in the series finale.
"If he's ready to go, we'll play him tomorrow," Cubs manager Lou Piniella said.
Jason Marquis (6-6) took the loss, giving up three runs on five hits over six innings. He served up Jackson's 10th home run with one out in the D-backs' first, and Mark Reynolds added a two-out RBI single in the third for a 2-0 lead.
"For the most part, I executed the way I wanted," Marquis said. "I feel positive, and hopefully we can get out of this funk and get out of our own way and play good baseball."
The Cubs tallied in the fourth when Mike Fontenot hit a two-out RBI triple, driving in Mark DeRosa, who had walked. But Stephen Drew gave Arizona a 3-1 lead with an RBI double in the fourth, and Hudson connected in the seventh off Sean Marshall.
The Cubs, who have been scuffling offensively, didn't hit on the field before the game. Some players did take some swings in the cage, some played cards, others watched the early games, including the Brewers-Cardinals contest. Piniella took a power nap in his office.
"It's good just to change it up," said outfielder Reed Johnson, who arrived later than usual to the ballpark. "We have to change something up, because whatever we've been doing hasn't been working."
But they were 1-for-9 with runners in scoring position Tuesday, and are now 1-for-19 in the four losses since the break.
"We're getting people on," Piniella said. "We're not getting them in."
"If he's ready to go, we'll play him tomorrow."
-- Manager Lou Piniella, on Alfonso Soriano
The frustration showed in the third. Chicago had runners at first and second with one out, but Yusmeiro Petit (1-1) got both Derrek Lee and Aramis Ramirez to fly out. Ramirez flung his batting helmet in disgust after the out. He was hitless in four trips to the plate, and is 0-for-21 since the All-Star break. Lee also grounded into his National League-leading 21st double play in the fifth and is 3-for-21 on this trip.
"We're struggling," Piniella said. "We've been struggling for a longer period than what you think. We've been able to win baseball games, but we haven't been scoring runs with the proficiency that we were much earlier in the season."
Struggling might be an understatement. Lee, Ramirez and Geovany Soto are a combined 4-for-60 in the last five games. Jim Edmonds had been one of the bright spots, but he had to leave the game because of a sore knee.
"We're better than the way we're playing," Lee said. "It's frustrating. Any time you don't score runs -- what is it, six games now? We just have to turn the page, relax and play."
So, after switching up the pregame routine, now what?
"You just keep playing," Lee said. "You have these stretches, and it happens. It happens. It'll turn around. We're too good of an offense."
The game got away from the Cubs in the seventh and eighth as Marshall and Kevin Hart were roughed up. The D-backs batted around against Hart, whose ERA ballooned to 7.91.
"Hart struggles every time he goes out there," Piniella said of the young right-hander. "He's not pitching with confidence. Outside of that, what can we do? We'll keep playing. Nobody feels sorry for us. We're going to have to play our way out of this thing. The one positive is we've had five well-pitched games from the starters."
On Monday, Arizona center fielder Chris Young seemed to catch every ball. On Tuesday, they were able to sneak a few hits in, including Fontenot's RBI triple. Daryle Ward notched his second homer, a pinch-hit blast, with one out in the eighth. That was it.
"The fact remains we've struggled offensively," Piniella said. "I was hoping we'd come out of the break swinging the bats. If we were swinging the bats on this road trip, we'd have a real nice road trip. Things go in cycles, and you have to take the good with the bad in this business."
It is early, and there's a lot of season left.
"That's why we can't press too much," Marquis said. "We know we have enough talent in here to get it done. We can't go throw our gloves on the field and expect to win. We have to execute pitches, have good at-bats, execute at-bats, move runners over, get guys over. It's just getting back to basics and playing good, fundamental baseball."