FiveThirtyEight has a projection model for the playoff seedings, and the Bulls are currently given a 19% chance to make the playoffs. Their projection is a 40-42 season putting them in 9th, 3 games behind the Pistons for the final seed.
They're currently a single game behind the Pistons, and 2 behind the 7th seeded Indiana Pacers.
Before the Pacers lost last night (changing their playoff odds from 97% to 95%), TheAthletic broke down the remaining schedule and FiveThirtyEight's work:
The Bulls, for example, play only eight of their last 18 games at home. Meanwhile, each of the East’s other playoff stragglers play a majority of their remaining schedules at home: Atlanta, 9 of 16; Indiana, 11 of 17, and Detroit, 11 of 16.
On top of an unfavorable mix shift, the Bulls have lost their last eight in a row, and 20 of 31, away from the United Center. Detroit also gets the benefit of a cozy nine-game homestand after its Monday night game at Washington. All four teams have reasonably favorable schedules with sub-.500 opponent winning percentages.... only two of Detroit’s final 16 games will feature a contest in which the Pistons have less than a 55 percent chance of winning that game: Oklahoma City and at Orlando.
This surmises it's actually Indiana who the Bulls may have the best chance at catching, as their schedule has more 'toss-up' level games that could go against them. And as for the Bulls...
The Bulls would need to win several games they will not be favored in, such as this Wednesday at Washington and the following Wednesday at Madison Square Garden. They will also need to win each of their games against the teams in their cluster (Detroit, Atlanta, and Indiana) whom they each play once more and in which they will be the favorite only once.
Obviously, the model doesn't 'know' how healthy the Bulls are going to be down the stretch. It's not looking good. Getting everybody healthy and ripping off a long win streak is possible, but you can understand why it's not considered a likely outcome.