I'm trying to minimize my federal income deductions to as close to zero as possible. That's because between my deductions and credits, I owe no federal income tax. As it stands, I usually get a sizable federal refund and I'm not interested in an even bigger refund.

I'm at 20 exemptions on my W4 and it's still not enough to wipe out the tax. What should I do?

“I'm trying to minimize my federal income deductions to as close to zero as possible.”----->As you can see, deductions reduce your taxable income(so minimizing your federal tax deductions increase your taxable income on 1040 line55 and 60), and therefore can be useful strategies for reducing your US federal income tax. Some deductions can be claimed directly on the tax form itself, while other deductions are available only if you itemize or have certain types of income. So, to reduce your tax refund, you need to minimize your tax deductions by taking standard deductions instead of itemizing deductions on Sch A.
“That's because between my deductions and credits, I owe no federal income tax.”---->Correct.
“As it stands, I usually get a sizable federal refund and I'm not interested in an even bigger refund.”------> Agreed; tax refund should not be considered free money. If you do receive a large tax refund,as you said, you are essentially giving the government a tax free loan. If your refund is over $5,000 every year, that’s over $400 every month that you are loaning the government without them having to pay you a dime of interest(as of March 2011, the IRS says the average tax refund check now tops $3,100) . If you usually receive a large refund, in common sense, it would be wise to look at your deductions you have marked on your W-4 with your employer. If you change your deductions and have less deducted from each check you could either use that on other expenses throughout the year or save it and use it to buy something like you use your tax refund.
“I'm at 20 exemptions on my W4 and it's still not enough to wipe out the tax. What should I do?”----->Fundamentally, the goal to break even between fed tax liability on 1040 and taxes withheld on W2, at the end of the year is almost impossible(with the complexity of our tax system, the precise amount of withholding to take is an inexact science, at best. ) .I guess first, you need to fill out a new W-4 form with your employer to change your tax withholdings (in order to have less taxes withheld every month), and therefore increase your take home pay. To minimize the amount withheld and prevent yourself from having extra withheld, you should claim as many allowances as you are entitled to based on your W-4 personal allowances worksheet. The number of withholding allowances claimed on W4 may differ from the number of exemptions claimed on your taxreturn on 1040.As long as you have other income that does not have taxes withheld from it, then you need to reduce portfolio income,i.e, interest or dividends income to prevent claiming fewer allowances on your W-4. Unless you have significant other income, or prefer to receive a large refund check at tax time, you should claim as many allowances as you are entitled to claim. This will minimize the amount of overwithholding. In general, REMEMEBR:every year, in order to avoid being charged interest and penalties for underpaying your taxes, you may pay (or have withheld) the smaller of: (1) 90% of your current year’s tax liability, or (2) 100% of the previous year’s tax liability .