I can't pay the full amount of the federal taxes I owe. Can I make a partial payment now and pay the rest later?

yes you can. but it's probably best if you set up a payment plan.

https://www.irs.gov/payments/online-payment-agreement-application 

In the TT program ... in the FILE tab you cannot make a partial payment ... it is all or nothing.   So choose the "mail a check" option so you can efile the return then  either mail in a partial payment  OR  pay online on the IRS site here : https://www.irs.gov/payments

You can also set up a payment plan  if you wish ... click on that blue button and make an initial payment with the application.