Do I need to claim rental income even if the payment barely covers the mortgage?

Whether your rental income is more or less than your rental expenses is not relevant.

If you have a rental property then you are required report all rental income received and all rental expenses to include the rental property depreciation on Schedule E.

Our mortgage payment is $699 and she pays $725

That's irrelevant and doesn't matter. Your mortgage payment isn't a deductible expense anyway. Only the interest you pay on that mortgage is a deductible rental expense.

But if you'll work this through the program the way it's designed and intended to be used, you'll find that you won't pay one single penny of tax on the rental income.

That's because when you take into account the depreciation you are required to take by law and add to that the mortgage interest, property taxes and property insurance deductions, those four items alone will "easily" exceed the total rent you collected for the year. Add to that your allowed rental expenses for things like repairs, cleaning and maintenance and I can practically "guarantee" you that not one single penny of your rental income will be taxable.

When done with the SCH E section if you'll look at line 26 of that SCH E you'll see it's a zero or a negative number indicating a loss.