Definitely not, at least not if you want to re-enter the U.S. as what you are, a full-time resident of the country. Section 215(b) of the Immigration and Nationality Act spells it out pretty clearly: "Except as otherwise provided by the president and subject to such limitations and exceptions as the president may authorize and prescribe, it shall be unlawful for any citizen of the United States to depart from or enter, or attempt to depart from or enter, the United States unless he bears a valid United States passport." That's not to say that U.S. citizens cannot use foreign passports when traveling abroad - for example, you could use your Irish passport if you were going from Ireland to France. Having the Irish European Union passport certainly does facilitate easier travel in some instances. However, one of the greatest benefits of becoming a U.S. citizen is the right to apply for an American passport, which allows for virtually unfettered access to the U.S. at any time from trips of any length abroad. If you were to re-enter the U.S. on an Irish passport, you would be presenting yourself as a short-term visitor, when in fact you are an American citizen resident. The problems in that scenario are obvious. Having said that, the possible penalties are fines as opposed to anything more serious, but to avoid any hassles whatsoever, it really is best to conduct inbound and outbound travel to the U.S. with an American passport. You say your travel plans are imminent, but given that you can still obtain a passport in two weeks, and even quicker in emergencies, you should have time to obtain your American passport, which will save you much grief down the road. For more on passports, visit http://travel.state.gov. Travelers can check the status of their pending passport applications online at this address as well. Information is normally available online approximately four weeks after the application is submitted. The National Passport Information Center can also be reached by toll-free phone at 1-877-487-2778.
What Irish phrases you need to learn before you visit Ireland