Odds of Getting In
If you get into a midwifery program, you've already gotten your foot—plus a good portion of your leg—in the door. Because they want an intensive faculty-to-student ratio and because there are many more applicants than spots, CNM programs can be quite selective (source). That's a really good thing if you get in, because it means they're already certain you have what it takes.
It also means the vast majority of prospective students are rejected the first (or second, or third) time they apply to a nurse-midwifery or midwifery program. If you want to be accepted, it's all about the nursing degree.
Once you get into the program, you'll probably get the intensive attention and internship experiences you need to find a job in the real world. Even with this extra help, you're going to have to be a little more proactive than just putting up some business cards on your local health center's bulletin board; that's how people find babysitters, not baby deliverers.