Can I get my taxes direct deposited into my savings account?

Yes as long as you have a routing number and account number for the savings account. Under the file heading you will be asked to enter in your direct deposit information (this is where you provide the routing and account number). 

I selected a checking account option and accidentally input my savings account routing and account number. Will this cause an issue for my direct deposit?

@Kgreen89

If a bank routing number and account number was entered correctly, it will go there. 

Please see this Turbo Tax FAQ on IRS refund methods. https://ttlc.intuit.com/community/refunds/help/what-are-the-different-options-for-getting-my-federal-irs-tax-refund/00/26249