Short Answer
The dollar amount of a criminal tax offense is considered at the sentencing stage, but is only one of many factors and merely helps determine which of several possible sentencing guideline sentences that a U.S. judge uses as a starting point when determining the sentence.
While the amount of money involved is a factor, the punishment isn't usually "proportional" to the tax liability in a criminal tax case.
But criminal tax offenses make up only a tiny fraction of all punishments imposed for violating tax laws. Most tax law violations are punished with civil penalties that are often proportional to the amount of tax not paid or not reported.
The U.S. pattern in this respect is typical of punishments for violating tax laws in the developed world more generally.
Undeveloped and developing country economies tend to be less bureaucratic and to have a more criminal law oriented system for punishing violations of their revenue collection laws, and also tend to have narrower tax bases limited to more concrete transactions. Many resource rich countries, like oil rich monarchies, often don't impose taxes on the general public at all.
Long Answer
I'm sure they will punish me somehow, and not care about any
explanation I might have. But will the punishment be 40 years in
federal maximum security prison, even though the amount of money is
ridiculously small? Or will they just tell me to pay it and perhaps
add a $20 fee on top of the 30% of $500 that they consider me to owe
them?
When Are Tax Crimes Prosecuted?
The vast majority of the time, when you don't pay your taxes, tax collection authorities impose a monetary civil penalty, which often is proportional to the amount of money at stake, rather than punish your non-compliance in the criminal justice system. Less frequently, the civil penalty involves the forfeiture of property of the offending taxpayer (e.g. currency received as lawful payments for goods or services that is not disclosed to tax officials), or the loss of some tax law related benefit or privilege (e.g. disallowing a tax credit when a tax return upon which it should be claimed isn't filed by the due date).
Strict liability or negligence based penalties for tax law violations are usually civil rather than criminal. Criminal penalties for tax law violations are usually reserved for intentional misconduct.
How Severe Are Tax Crime Penalties?
Criminal tax crimes usually involve intentional fraud or willful conduct influencing the amount of taxes you owe (as opposed to good faith efforts to lawfully not pay higher taxes than necessary, or negligent or unintentional actions that have that effect), or intentional non-reporting or misreporting of information necessary for the government to determine how much tax someone else owes, or willfully failing to pay or collect taxes when the taxable is able to pay or collect the taxes, or for conduct that thwarts tax collection more generally (like sending fake inaccurate tax forms to random people causing them to pay the wrong amount of taxes or none at all). The maximum penalty for serious tax crimes of this type are typically similar in severity to the maximum penalty for non-violent theft, forgery or fraud offenses not involving taxes, which is typically at the low to medium end for felony criminal conduct and is typically far less than the maximum punishment for violent crimes.
Crimes involving willful manipulation of how much tax is owed by someone usually has higher maximum criminal penalties than willful failure to pay or collect taxes.
Conduct such as lying to tax investigators, or disregarding legal process during tax audits and litigation, or other fraudulent conduct that doesn't change how much is owed or paid directly but makes it more cumbersome to collect taxes (like intentionally filing a false information tax return, when the taxpayer reports the income anyway, or filing a false information tax return to harass someone who doesn't owe any tax in the first place), are typically misdemeanors with only comparatively minor criminal penalties (perhaps a few days to a year in jail and a fine in the hundreds or single digit thousands of dollars).
The main driver of the maximum penalty for the narrow range of tax law violations are actually tax crimes is how clearly malicious and unruly the conduct is, rather than the amount in controversy. Negligently failing to pay $10,000,000, or recklessly taking a very dubious tax law position in a tax return, will usually result in a large civil tax penalty, but no criminal prosecution. Intentionally forging or doctoring a $700 information tax return, or intentionally paying a tax bill with counterfeit currency, will usually have criminal penalties.
There are also quite a few crimes that arguably count as tax crimes for conduct like murdering tax collectors, kidnapping tax collectors, assaulting tax collectors, bribing tax collectors, blackmailing tax collectors to act unlawfully, stealing or destroying tax collection agency property, etc. that would be crimes even if there was no tax component to the conduct, that I do not consider in this answer. These crimes are usually punished only modestly more severely than they are in the non-tax context when no government officials or offices are involved, and are usually punished with about the same severity as other crimes against non-tax government officials.
Determining The Sentence For A Tax Crime Under U.S. Law
In the U.S., the maximum period of incarceration for a federal tax related crime is usually not related to the amount of money that the government was denied in tax revenues, although the civil penalties for violations of tax laws are usually capped at a percentage of the tax not paid. Criminal fines for tax offenses are sometimes related to the dollar amount of the offense, and sometimes aren't related directly to the dollar amount, although they may be determined with the dollar amount of the offense in mind.
The length of the sentence of incarceration and the amount of the fine actually imposed by a federal judge upon a conviction for a federal tax related crime between the maximum and minimum sentences authorized by law is governed by the U.S. Sentencing Guidelines set by the U.S. Sentencing Guidelines Commission.
The guideline sentence is based upon the specific subsection of the federal tax crime for which you were convicted and then a lot of factors that add or deduct points. Some of the points are related to your prior criminal history. Some of the points are related to your conduct in the litigation (e.g. did you cooperate with prosecutors), and some of the points are based upon the nature of the offense itself, including the dollar amount of the tax loss caused by the crime. Typically, there are several dollar ranges for each crime, and the number of points added to the number used to determine the sentencing guideline range is stated for each of the possible range of dollar values of the money at issue in the crime.
The number of points you have after the judge evaluates all of these factors (based upon a preponderance of the evidence with lower evidentiary standards than those that apply at the guilt-innocence phase of the case) to produce a non-binding recommended sentencing range for the crime. The judge than imposes the sentence.
A sentence within a correctly determined sentencing guideline range is always upheld on appeal. A judge can impose a sentence that is higher than the guideline range but lower than the maximum statutorily authorized sentence, or below the guideline range by higher than the minimum statutorily authorized sentence, if the judge articulates reasons for doing so that are on a list of reasons that a judge can impose a non-guideline sentence.
If a sentence for a federal tax crime conviction is appealed, the appellate court evaluates whether the sentencing guideline range was determined correctly, and whether if the judge imposed a sentence outside the sentencing guideline range, if the reasons articulated by the judge were insufficient to justify that decision and hence constituted an abuse of discretion by the judge. If the appellate court makes that determination, the case is remanded for re-sentencing in accordance with the appellate court opinion (assuming that the conviction itself was affirmed on appeal).