Applying from a different country: can the application be dismissed because of interview expenses?
In short, the answer is that yes, a search committee (or the administrators who would have to pay for the travel) could decide not to invite someone to an interview or invite them without agreeing to pay their travel expenses.  I don't believe that there's any legal requirement under US law to reimburse applicants for travelling to an interview, and I've seen some institutions (mostly community colleges) refuse to pay any travel expenses.  A more common thing is to reimburse only for travel expenses within the US (so you'd be responsible for paying your own way to New York or LA.)    What will happen in any particular case depends on the practices of an individual institution.   

If you are planning a trip to the US for some other reason, you might mention in your cover letter that you'll be in the US and could do an interview as part of that trip.