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Does an employee have the right to pay the federal and state taxes themselves instead of having employer doing it?
You can file a revised W-4 with your employer claiming more allowances than you do now. More allowances means less Federal tax and (if applicable and likely with a separate form) less state tax. This doesn't affect social security and Medicare with holding, though.  That being said, US taxes are on a pay-as-you-go system. If the IRS determines that you're claiming more allowances than you're eligible for and not paying the proper taxes throughout the year, they will hit you with an underpayment penalty fee, which would likely negate the benefits of keeping that money in the first place. This is why independent contractors and self-employed people pay quarterly or estimated taxes. Depending on the employer, they may require proof of the allowances for adjustment before they accept the revised W-4.