It kind of depends on how you interpret "going directly to the animals". While there is a lot of money that goes into the operations of the shelters themselves, that money is going to benefit the animals in the end. Power, for example, ensures air conditioning and heating for the kennels. The shelter I've worked with uses extensive volunteer labor to ensure that as many animals as possible can be saved.
Having said that, per charitynavigator.org the ASPCA spends about 36% of it's overall budget on fundraising. The local SPCAs spend quite a bit less then that. (Mine limits it's fundraising expenses to 10% of it's total budget). All of the rest of the money goes either directly to support the animals or to support outreach and educational programs that can prevent future cruelty.
If you are concerned about where the money is going, you can always donate directly to your local SPCA, drop off goods (toys, collars, leashes, blankets) or better yet volunteer.