Since she has 6 W-2s everytime she changed the job, the taxed were calculated based on the income that she earned from that job disregarding the income from the prior job. Hence, she did not have any federal withhold and very low State tax withholding since her income from that particular job(withhout considering her other income) was too low.
Unfortunately, this being the reason you may owe tax.
Let me know if you have any question.
Please note: This advice is provided with the understanding that all the relevant facts have been provided by you. Any change in facts might affect the advice given and hence may not be relied on in such cases. Nothing contained in this reply was intended or written to be used, can be used by any taxpayer, or may be relied upon or used by any taxpayer for the purposes of avoiding penalties that may be imposed on the taxpayer under the Internal Revenue Code of 1986, as amended.
It is normally dependent on the total income. So if you claim one allowance than the amount upto the personal exemption is not subject to tax. So if she makes upto $3300...no federal tax will be deducted.