Hi,

I have arrived to the US on 04 26 2010 as a J1 scholar (end date on my DS2019: 05 03 2011), this month I have received the new, extended DS2019 (end date: 05 03 2012). I tried to sing up for tax treaty of 2011 tax year and the payroll office said that is more than 2 years and the treaty reads "is invited" for a period NOT to exceed 2 years. So it means that I no longer have tax treaty or I have till 04 25 2012? I could claim for my money or not?

Claim the two year tax exemption; see extract from the technical explanation of the U.S.-Hungary Tax Treaty for Article 17 (Teachers). Note the sentence in RED.

The Article provides that when a resident of one of the Contracting States goes to the
Other Contracting State for a period not expected to exceed two years for the purpose of teaching or engaging in research or both at a university or other recognized educational institution in that other State, at the invitation of that other State or of a recognized educational institution in that State, the income for personal services of teaching or research at that educational institution shall be exempt from tax by the host State for a period not exceeding two years from the date of arrival in that State. This exemption does not apply to income from research carried on primarily for private benefit. If the two-year period is exceeded, the exemption is not lost retroactively; it will still apply to the first two years. However, to qualify for the exemption, the individual must have gone to the other Contracting State for a period which was not expected to exceed the two years.

Based on your posting, you clearly meet the criteria. At most, you will pay taxed for ONE week worth of work.