No effect at all - at least not a negative one. Regardless of the day the baby was born in 2017, when listing them as your dependent on your tax return, you will select the option to indicate the baby lived with you THE ENTIRE YEAR. Doesn't matter if the baby was born at 11:59pm on New Year's Eve. The IRS says you claim them for the entire tax year. This is going to automatically exempt an additional $4,050 of your income from being taxed, and it should be a bit of a help for you on the financial front with what it costs for diapers now-a-days.
Thank you! Does it have any effect that my withholding is still 1? or will that just reflect on my tax return?
The W-4 you filled out and gave to your employer goes not further than that. The W-4 is used by the employer, and only by the employer, to determine how much taxes to withhold from each of your paychecks. The IRS does not get a copy of your W-4, and if any employer sent the IRS a W-4, the IRS would just throw it away. THey have no need for your W-4.
When you file your tax return, item 6 (on the 1040/A) is where you claim your dependents and stuff, and it flat out doesn't matter what you may have put on your W-4. For me, I always reflected a lower number on my W-4 than what I could have claimed. That way, I almost "always" got a refund every year, and prefer that to the other option of owing the IRS money every year.
If you can, leave your W-4 as it is. That way, you get something back every year for sure and it sure helps with newborns and toddlers in the house. Of course, if you need more money in each paycheck just to make ends meet, then you can update the W-4 with your employer and change your exemptions to 2. That means the employer will withhold less from each of your paychecks. That also means that, depending on to many other factors to talk about here, you "could" end up owing the IRS come tax filing time. It could also mean you just get less of a refund than what you may be hoping for too.