Would a PhD from a foreign country hurt you in U.S. academia in terms of job offers? I'm about to graduate from a terminal masters program in the United States.  The most prominent PhD program I've gotten into has been at Trinity College Dublin.  I want to go into U.S. academia rather than Irish academia, but the PhD programs I've gotten into the U.S. have been second-tier.

Is there a disadvantage in terms of hiring prospects?  My main concern is that I might not be taken as seriously in the U.S. since European graduate schools have very short (by U.S. standards) periods of study.  I've heard 3 years of graduate work is typical for Irish universities in my field, while U.S. schools you might study twice as long.  

tl;dr First-tier Irish university or second-tier U.S. university for my PhD?
1) I don't know what you mean by second-tier, but TCD isn't at the level of Harvard/MIT/Princeton/Berkeley.

2) The answer does depend on what your range of acceptable careers post-PhD is, because the answer is different for different segments of the job market.  For research positions, it won't matter much, though you have to be careful not to work in an area that is poorly represented in the US.  For primarily teaching-oriented positions (and many US PhDs in mathematics take a teaching position, permanent or temporary, straight after finishing - certainly more than those who take postdocs), you are unlikely to be considered a serious candidate without US (or at least North American) teaching experience.