With the increase in days off that exist in the playoffs the bench (not literally) shrinks. You no longer need guys that can eat the middle innings, you need three guys that can take the ball from your starter for the 7th, 8th, and 9th innings to finish a game up. You need a trusted inner circle of relievers that can get the job done.
The Cubs do not have a deep bullpen. However, they do have five legitimate back end bullpen pieces and a potential sleeper that could bring the filth when needed. In an ideal situation, the Cubs would hand the ball from Stroman to Fulmer for the 7th, to Leiter for the 8th to Alzolay for the 9th. However, they also have the ability to go to Julian Merryweather and Daniel Palencia in the 7th or 8th if necessary or have Fulmer come in earlier if a starter gets into some trouble.
The Cubs are tied for the lowest number of blown saves in the majors this year. This is what a playoff team looks like.