You can claim whatever you want on your W-4. The only entity on the planet that gets that W-4 is the employer, and that's it. The employer uses the W-4 to determine how much taxes to withhold from each of your paychecks, and that's as far as it goes.
But at tax filing time what you put on the W-4 doesn't matter. What matters is what you claim on your federal and state tax return(s). So in a case where sufficient taxes were not withheld from each of your paychecks for federal and/or state, an under withholding penalty will be assessed in addition to the taxes you will have to pay at tax filing time.
On the federal side the general rule is that if at tax filing time you owe the IRS more than $1000 or more than 10% of your total tax liability (whichever is *HIGHER*) then you will be assessed an under withholding penalty in addition to the taxes you will pay at that time. I can't speak for the state(s) though, as each of the 37 states that tax personal income have their own rules on this.
