IT might hinder your chances. You should really talk to them before/during the second interview. Don't waste your or their time. If they are looking for a person to work for them for a longer period than your authorization, than you know what to do. This being said, they should not require from you more proof of your ability to work than they would from a US citizen. Maybe they will sponsor you for a work visa? You will have to disclose your status before they hire you 100%, imagine what it will be if you don't tell them up unitil the last second.
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Your question presents a character issue as much as a visa issue. Put yourself in the position of the prospective employer. How would you react if after interviewing multiple applicants, you belatedly discover that the applicant of your choice has only a limited period of employment authorization? Such a situation may result in disqualification on the basis of absence if trust. On the other hand, if you are straightforward, and the best candidate, chances are that you would be selected and the prospective employer would be willing to process the required visa for you.
The herein content is for general informational purposes only, and may be predicated on incomplete facts. It should not be relied upon in making legal decisions or assessing your legal rights or risks. Neither does the herein reply create an attorney-client relationship.