If I have to take an early withdrawal from my 401k. I have calculated the 10% early withdrawal tax, 25% federal tax and will I get taxed again come income tax time?

You are only taxed on your tax return. Just like with W2 or any other income, you withhold tax to account for its impact on your tax return. You are not taxed when you withhold, as your actual tax liability can only be determined on your tax return.

That being said, holding 35% (25% for tax and 10% for the penalty) is better than many others do. Provided that the true tax rate of this income fits a 25% rate, your withholding should have something close to a break even impact.

Just keep in mind that certain tax credits can lower because of additional income. This can make the tax impact effectively much greater.

Is your other income going to be similar in 2017? If so, add a "pretend" 1099R in 2016 to help estimate the true impact.

You didn't actually pay the tax or 10% penalty (you pay a 10% early withdrawal penalty if you are under 59 ½).  You had taxes withheld like from your paycheck. You still have to enter the whole amount (before taxes were withheld) with your other income to figure out the total tax (and it may put you into a higher tax bracket)  and then the withholding is subtracted from the total tax to figure your refund or tax due.  The withholding will show up on 1040 line 64 or 1040A line 40.  The 10% penalty is on 1040 line 59.

So the witholding might not be enough to cover the increase in income.