If you are for some reason looking for a ticket to prison, failure to pay taxes is not the fastest train to the destination...but it may get you there in time. You'll be hauled away and locked up much sooner for a reckless driving. But if you deliberately plot and plan to illegally evade taxes, the IRS is not happy and will use any method at its disposal, including criminal charges of tax fraud or tax evasion, to get the bucks you owe.
TL;DR (Too Long; Didn't Read)
While you can't go to jail for tax errors or for not having the money to pay taxes, you might be charged with tax fraud or tax evasion if you act deliberately, and these criminal charges can land you in jail.
Honest Mistakes or Sloppy Returns Are Not Crimes
Neither honest mistakes nor sloppy, negligent mistakes will get you a jail term. If you had a greenback for every error U.S. taxpayers make during one tax season, you'd be a wealthy person. In these cases, the IRS simply corrects the mistake and sends you a tax statement with the new, higher tax assessment. This is a civil matter, and although the IRS has many civil weapons at its disposal, from wage garnishment to tax liens on your real estate, it won't put you in handcuffs.
On the other hand, under Title 26 USC § 7202, the IRS has the power to charge you with a felony for willful failure to collect, account and pay taxes. This is applied when you are an employer and are supposed to withhold taxes from your employees' salaries and send them to the taxing authorities. It can be a felony charge and send you to jail.
Dealing with Taxes if You Don't Have the Money
Likewise, you can't go to jail for not having money to pay the taxes you owe. Your best bet is to be upfront with the tax agents. If you are judgment-proof (without assets that can be collected), the IRS will confirm it, and often put liens in place in case you ever get any money, and that will be that.
If you aren't exactly broke but you don't have enough to pay your assessment, you have options. You can work out an installment payment arrangement, making small monthly payments that will pay off the bill in three years or less, plus interest. You can ask for a hardship suspension, in which you don't pay because you are going through hard times, but interest accrues and Big Brother keeps an eye on your finances, waiting for a flush of luck. You can also offer to pay less than your assessment in a lump sum as full payment on a larger tax debt. If accepted, this is called an offer in compromise. Or, you can file Chapter 7 bankruptcy and try to wipe out income tax debt.
How Long Can You Go Without Filing a Tax Return?
Failure to file a tax return won't always land you in jail, but it can. If the IRS has evidence that you actually earned money and owe taxes, say via 1099 forms or similar reporting mechanisms, it will more likely hit you with an assessment.
However, it has the power to charge you criminally for failure to file a return under Title 26 USC § 7203. The penalty can include up to one year in jail the very first time you do it, so don't play a game of Russian roulette to see how long you can get away with it. If you are just not ready to file, you can get an extension of time by filing a simple extension request with the IRS, but you'll still have to pay estimated taxes on time.
How to Get a Deadline Extension on Filing Tax Returns
File IRS form 4868 for an automatic, six-month extension to file your tax return. You are supposed to pay estimated taxes before the initial tax deadline, however, so you may get hit with penalties and fees if your estimated tax payments total significantly less than the amount you owe.