I am a post-bac at NIH. With any NIH program, the earlier the better for applying. I am sure it is still possible to find a lab, but it is hard. You need to email potential PIs about potentially working with them and attach a resume. This is a common mistake people make when applying to NIH programs. You may have to send this email to 20+ faculty to find one with an opening. Some PIs, including mine, only take in people that send emails expressing interest in their work.
From my experience, most PIs only take Freshman and occasionally sophmores so they can keep them for a few summers. If you are a junior, I would not count on finding a lab (but it still may happen). If you are interested in doing a post-bac, I would list this as another possible persuasive point to take you in. They want to get significant amount of work from you, if they are going to train you.
I applied to around 10 internships during spring break last year (mid-late march) and still ended up being accepted to 3 of them. Obviously, with internships, the earlier the better but it's still not too late.