Here's the trade I have in mind:
In essence, the trade is Asik for JR Smith, though to make salaries work the deal has to be much larger:
Asik, JJ, Bogans, Scal for JR Smith, Ely, Carter, Forbes
I think it would be very difficult for the Nuggets to turn this down. They get a promising young center and cut over $3 million off the payroll in exchange for JR Smith and expiring contract filler. They can go with a 3-man backcourt rotation of Billups, Afflalo, and Lawson without much of a dropoff in performance. If the Nuggets think JJ has positive value, it's even better.
In addition, this trade could be very good for the Bulls. JR Smith is probably the best SG available right now. He can shoot, and he can score off the dribble. While Bogans struggles to keep his Usage above 10%, JR is consistently at or above 20%. His much higher usage would take pressure off of Rose, Deng, and Boozer. Though he's not known for his defense, he's big and athletic for the position, and his defense has typically been good by the metrics (sub-15 opposing player PER each of the past 3 seasons according to 82games.com).
How much would the Bulls miss Omer? I really like him, and I think he's generally a fan favorite. However, Asik has played less than 5 minutes in 5 of the last 9 games. When Noah comes back, it's unclear if he'll play at all. Even if Kurt is done after this year, Taj seems to be a perfectly acceptable backup Center. Deng has also been quite effective as a stretch 4, so the Bulls shouldn't struggle to fill the frontcourt minutes when at full-strength. Adding a reasonably competent big man through the draft or as a minimum salary player to be emergency depth shouldn't be particularly burdensome either. Ely will fill that role for the remainder of the year.
Another issue is whether JR would negatively affect the team chemistry. He was held out of a game a few days ago for disciplinary reasons after being late for a team shootaround. His conduct seems to have raised a red flag for the Bulls a few years ago. Would Rose, Noah, etc. be able to keep him focused? Would he buy into Thibs's defensive scheme? If so, I think he could make the Bulls significantly more dangerous in the playoffs against the top teams. At least if he's added to the team now, the Bulls can try him out for a few months before deciding if it's worth offering him a contract in the offseason.