Not necessarily. Property tax is only one of all the possible itemized deductions.The program starts out by giving you a Standard deduction. You won't see any change in your tax owed until the total of all the itemized deductions you enter exceeds the standard deduction amount. You only get to take one or the other. If you have more itemized deductions to enter, continue on.
There also is the fact that property tax is added back for the calculation of AMT, so, if you owe AMT, you'll see no change in the tax owed.