Most countries with income tax, including the USA, design their withholding system so that in straightforward cases, tax is withheld from each month's paycheck on an annualized basis: tax for a month is calculated on the assumption that you will keep earning the same monthly amount for the rest of the year, and the withholding is set so that the tax is spread evenly across the year.
Another way of putting that is that in practice you only get the tax brackets allocated proportionately throughout the year - so up till the end of August you'll only have been assigned 8/12 of the $37450 bracket, and so on.
So if your income doesn't change and your general tax affairs don't change, your paycheck also shouldn't change.
If your income is irregular or changes during the year
then things can get more complicated. As other answers have noted, withholdings are calculated according to tables that normally just take into account that specific month's income.
There are various possible changes to your tax affairs that might cause the withholdings to change. For example there'd be an impact from any change in your contributions to tax advantaged things like health insurance or retirement, health or education savings. You might also use form W-4 to change your withholdings yourself.
Note that even with a regular income that doesn't change through the year, you might find yourself either owing money or being owed a refund when you file your taxes after the end of the year. It's worth making sure that your W-4 accurately records the allowances you are entitled to, to minimize or eliminate this adjustment.
Category: Personal Finance