I understand that owe $407 to federal this year. I see that $6060 was taken from my husbands check for federal. Would we still owe if I would've had federal taken out?

Yes you can have enough withholding to cover the tax due and even get a refund.  Apparently the withholding wasn't enough to cover the tax due on all your income.  He might need to change  his W4 for work.

https://www.irs.gov/pub/irs-pdf/fw4.pdf 

What you claim at work on the W4 doesn't have to match your actual tax return filing status. It's just to tell your employer how much to take out. You will get credit for all the withholding on your tax return. I'm married but claimed Single on the W4 to have more taxes taken out.

Oh, you have income too?   Yes you should have withholding taken out of yours.  Or just increase his to cover the total income for both of you.  

Yes, if your household has multiple incomes, you should have taxes withheld from all of them.

You both should provide a W-4 for your employer to withhold the proper tax.

Your combined incomes are like a ladder for your taxes.  Each income is added on top of the other.

If you have multiple incomes, your taxes will go up rapidly.

Taxes start at 10% and go up to 37%.  I'll show fewer tax brackets for simplicity.

For Married Filing Jointly

$0 to $22,000 - 10%

$22,001 to $89,450 - 12%

$89,451 to $190,751 - 22%.22

If your married and both of you work.

You both have taxable income of $50,000.

You get taxed at 10% for $22,000 = $ 2,200

And at 12% for the next $30,000 =  $3,600

Your spouse is taxed 12% in $37,450 = $4,497  (the balance in the 12% bracket

Finally she will pay 22% on the last $12,550 = $2,761

For a total tax of $13,048

The W-4 has to show how the income accumulates, and must be complected for all sources of income.