How do I file taxes from two states when the sum is greater than my true total federal income?

That can happen when certain states (such as PA) tax income that is not taxable for federal purposes.  An example is 401(k) contributions, in some states you can contribute to this tax free like the federal and in other states it is not a tax free amount. 

Some state returns begin with the federal income while other state returns begin with their own income categories and allowable adjustments or deductions. 

That being said, it depends on the states that you are required to file.  In general, if you are using a W2 from the same employer or more than one employer and your employer(s) listed a total for state wage for two different states combined that is greater than Box 1, for your total gross wage, then you should figure out the actual taxable amount of wages for each state that can be reconciled with box 1 on your W2. 

Again, depending on the states, it can occur based on what is included (or excluded) from the gross wage. If you don't have any special tax free deductions from your wages, then you shouldn't have a difference in your combined state wages against the federal return. 

If you are a full year resident in one state and have earnings from another state the following information will explain how that works.

Resident State:  All income worldwide is required to be reported on your resident state return.  Any money that is also taxed in a nonresident state is eligible for the "credit for taxes paid to another state" when you complete your resident state return.  Your resident state does not want you to pay tax twice on the same income.

Nonresident State: Any money earned in a nonresident state is required to be reported on that state tax return (with the exception of reciprocal agreements).  The nonresident state will tax any income earned from that state.  

Finally, the information below will explain what a "reciprocal state" is (only pertains to wages, not other types of income such as interest or dividends).

https://ttlc.intuit.com/replies/3299954

If you have multiple W-2s from an employer, try combining them into one entry in TurboTax in your Federal return.  Then go through your STATE interview again and try efiling. 

Click this link for more info on Multiple W-2s.