The FSA has nothing to do with your tax return.
Make sure that when telling the estimator the amount of your wages you enter only the taxable amount of wages, not the gross amount of wages before deductions for elective deferrals to the 457(b). There are some things that these estimators do not take into account, but these are usually things that, if not considered, would cause it to estimate a greater refund or smaller balance due, not the other way around.
There should be no significant difference between working in the private sector and making elective deferrals to the employers 401(k) and working in the public sector and making the same amount of wages and the same amount of elective deferrals to the 457(b). Perhaps you somehow specified at the new job that less taxes be withheld, increasing your balance due.
You would get a much better estimate by using TurboTax to prepare a simulated tax return. You would generally want to use the CD/download version of TurboTax, not the online version for this.
