W4

You can claim whatever you want on your W-4. The only entity on the planet that gets that W-4 is the employer, and that's it. The employer uses the W-4 to determine how much taxes to withhold from each of your paychecks, and that's as far as it goes.

But at tax filing time what you put on the W-4 doesn't matter. What matters is what you claim on your federal and state tax return(s). So in a case where sufficient taxes were not withheld from each of your paychecks for federal and/or state, an under withholding penalty will be assessed in addition to the taxes you will have to pay at tax filing time.

On the federal side the general rule is that if at tax filing time you owe the IRS more than $1000 or more than 10% of your total tax liability (whichever is *HIGHER*) then you will be assessed an under withholding penalty in addition to the taxes you will pay at that time. I can't speak for the state(s) though, as each of the 37 states that tax personal income have their own rules on this.

...............and Iowa gets the first call on taxing the wages at that Iowa W-2 job on the IA non-resident tax return. 

 Then, you will get a credit on your NE tax return for the taxes paid to IA when you fill out your NE Resident tax return (you will have to file both states).   So, in addition to the Federal W-4, you probably just need to fill out the separate IA-W-4 issued by the IA dept of Revenue as best you can.  (probably provided to you by your employer).  A NE-W-4 equivalent is probably not needed, and may not even be available to use at your employer anyhow (depends on the employer).

For taxable income below ~$3,100 (after deductions and exemptions), IA has a lower tax rate than NE.  So if the IA job is low paying for the rest of the year, and you have little or no other income from any source for all of 2019, the credit will not-quite cover any extra tax you may owe NE when you file early next year (but would still be pretty small).     IF the IA job results in taxable income higher than ~$3,100, then the taxes paid to IA will exceed the NE tax rate, and your potential NE taxes, on  that IA income, will be fully offset by the NE credit for taxes paid to IA.

You should note though, that the %tax rate IA sets for a nonResident is based on your total yearly income from all sources, and the final IA calculated tax, is ratio'd down in the final steps of it's tax return preparation, based on the % of income actually earned in IA.  So if you have a fair amount of other income for 2019, your IA tax on the IA income may be higher than NE anyhow...so you won't owe anything more to NE for that IA income.  Still, you may have other income in NE from a previous job in NE (or interest, or dividends, or investment capital gains...etc), and that other income can affect your NE taxes independently of your IA job.  You'll know better what to do to refine&reset your tax withholding for 2020, the first time you prepare and  file your 2019 taxes for Federal, IA, and NE in Feb-April of 2020.

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Other Notes:  In order for things to be done properly in the software, you will need to have your  Federal taxes fully filled out first with every scrap of income, and all deductions & credits for 2019 all entered and essentially complete (except for filing)....then the IA nonresident tax return has to be completed, and then the NE tax return last.  The IA non-resident tax return has to be done before NE, because the exact amount of IA tax liability has to be calculated before NE knows what the credit-for-taxes-paid-to-IA will be.

(And, the NE-credit is not the IA withholding on your W-2....if IA refunds some of their taxes withheld on your paycheck, the potential NE credit will be just what IA kept.... after the IA-refund.    Also, the NE-credit may still be a bit lower because NE only allows a credit for up-to what tax NE would-have charged you, and the NE tax rates are a bit lower than IA).