There are a number of different sides to this; the Irish people (as RBS will probably endorse ... although because of his rebellious nature he might just say a word that rhymes with 'rowlocks'

) have always been proud to be considered rebellious, the EU Treaty is a compromise to avoid having another attempt at an EU Constitution (some might say, "same old sh*t, different label"), the diversity of the EU compared to the US (laws, currencies, religions, and languages), and the fairly recent addition of many new member states.
I understand that Irish law dictates that any change to its constitution requires a referendum. Other EU member countries have different requirements. For example, the UK has no written constitution and has only ever had one referendum (in 1975).
Sovereignity is not up for grabs at present. BTW, there are 7 monarchies who are member states; Belgium, Denmark, Luxembourg, Netherlands, Spain, Sweden, and UK ... so it is not just the Queen Elizabeth who might be affected.
There is a host of information here:
http://europa.eu/abc/index_en.htm