When I enter the amount I paid for my child care expenses, the total amount on the "here's what we have so far" page is way less than the amount I entered. Why?

There are several reasons why this could happen but most likely your expenses exceeded the amount allowable for the 20% computation.  

f you paid work-related expenses for the care of two or more qualifying persons, the applicable dollar limit is $6,000. This limit doesn't need to be divided equally among them. For example, if your work-related expenses for the care of one qualifying person are $3,200 and your work-related expenses for another qualifying person are $2,800, you can use the total, $6,000, when figuring the credit..

Yearly limit.

The dollar limit is a yearly limit. The amount of the dollar limit remains the same no matter how long, during the year, you have a qualifying person in your household. Use the $3,000 limit if you paid work-related expenses for the care of one qualifying person at any time during the year. Use $6,000 if you paid work-related expenses for the care of more than one qualifying person at any time during the year.

Publication 503 Credit for Child or Dependent Care