James scored 11 straight points for Cleveland late in the fourth quarter and finished with 32 in the Cavaliers' 97-85 victory over the Milwaukee Bucks.
"They should," James said. "I have done it in the past, and I'm going to continue to do it in the future. And tonight was one of those games when they looked at me, and I took it upon myself to do that."
James struggled much of the night, going without a field goal for more than 15 minutes in the second half before he led Cleveland on a decisive 11-2 run. He was 12-of-27 from the field and the Cavs shot a season-low 41.5 percent.
Zydrunas Ilgauskas added a season-high 23 points and 17 rebounds to help Cleveland win for the 13th time in 14 games. Michael Redd returned after missing 14 games with a right ankle sprain to lead the Bucks with 20 points in 35 minutes.
The last-place Bucks have dropped four in a row.
Cleveland never trailed and dominated Milwaukee inside, outrebounding the Bucks 53-38. The Cavaliers had 22 second-chance points to Milwaukee's seven and 19 offensive rebounds to Milwaukee's seven.
"We stuck with it," Cavaliers coach Mike Brown said. "We could've folded at any time during the course of the game. We could have given a ton of excuses -- fourth game in five nights, things just weren't going our way shooting the ball.
"We stuck together."
James struggled much of the second half, scoring three points until his layup with 5:08 remaining made it 84-79. Two free throws and three more baskets later, including a 3-pointer, and Cleveland led 93-81. James finished with 14 points in the period.
"We tried three or four different coverages on him and, like all the great players do, he has a really good sense of timing of when to take over," Bucks coach Scott Skiles said. "In both games that we have played against him, we have struggled to contain him in any meaningful way. He's a great player."
Milwaukee had just one field goal in the final 4:51.
Milwaukee cut it two at 79-77, following Luke Ridnour's 3-pointer midway through the fourth quarter, but Sasha Pavlovic responded with a 3-pointer of his own to make it 82-77 with 5:43 remaining.
James then took over in the next 3-plus minutes.
"I had to be aggressive. The outside shot? It wasn't flowing tonight. We had great looks. We continued to take them, and we continued to miss them. We couldn't in the fourth quarter continue to not make open shots or not get into the paint. So I took it upon myself to just try and get into the lane and create for myself, create for others."
James had 14 points in the first half. He also made his presence known on the defensive end, blocking a Sessions second-quarter layup attempt into the second row of Section 201 and almost hitting a female security guard seated nearby.
Redd averaged 21.3 points in the first four games this season before injuring his ankle against New York on Nov. 2. The Bucks went 5-9 in Redd's absence.
"Rusty, rusty, just trying to get back into the swing of things, which is natural," Redd said. "Just got to continue to keep rehabbing it and keep getting it stronger. It felt great being out there."
Jefferson said it was good to see Redd back.
"Overall, even with him back, it was the same story," he said. "We just didn't get enough stops in the fourth quarter."
Milwaukee was without center Andrew Bogut, who missed his second straight game with a bone bruise on his left knee.
James had a season-high 41 points in the Bucks' first game against the Cavaliers on Nov. 11. Cleveland won 99-93. ... Ilgauskas was coming off a season-high 21 points on 9-of-13 shooting in Cleveland's 112-97 victory over Golden State on Friday. ... Mo Williams was making his return to Milwaukee after being traded to the Cavaliers in a three-team trade on August 13. He played four seasons with Milwaukee and averaged 17.2 points and 6.3 assists for the Bucks last season.