These are a few quick thoughts comparing 2004 with 2006:
1. Yes, Latinos shifted *more dramatically* than all other demographic groups, but since they are still less than 1/10 of the total vote, their impact was not as large. It was really a spectacular shift, but whites -- still 4 out of every 5 voters -- are the group whose swing made the difference. The impact of Whites switching from Rep to Dem was almost 4 times larger than the impact of Latinos. African-Americans didn't switch their votes, because they were also solidly behind the Dems in 2004. Black turnout declined a little as a percent of total turnout, perhaps believing their vote would not count. Asians also switched massively (not as much as Latinos, but massively), yet their impact was even smaller due to their small share in total voting population. So, in brief, Whites decided.
2. Young people switched votes dramatically and made all the difference, both because they switched their votes to the Dems w.r.t. 2004 and because they are 4 out of every 5 voters. That said, I should clarify here that my definition of "young people" is the widely-accepted definition in these lists of people below 65. The "extremely young people" (the category between 18-29 inclusive) switched votes dramatically (more dropping out of the Reps than joining the Dems), but their effective impact was a third the impact of the really young ones: 30-59.
3. By income, the votes that switched and made the difference were those of the not-poor working class and "middle class" ($50-100K). Voters declaring $100K or more dropped out of the Reps and joined the Dems faster than those with less than $100K, but they are only 1 out of every 5 voters. So, the difference was made by those with less than $100K.
4. People in households with union members dropped the Reps like a hot potato and joined the Dems just like everyone else, but they are 14% of the voters, so the difference was made by non-union people. By education, people with high school and some college (over half the voters) switched massively. Those with no high school switched their votes *much faster* from Reps to Dems, but they are 3% of the voters. Altogether, people with no college degree (55% of the voters) made the difference.
5. By religion, Jews switched votes the most, but they are only 3% of the voters. Protestants and Catholics (more Catholics than Protestants) switched allegiances and made the difference. Note the overlapping between Latino and Catholic. (Similarly, note the overlapping between married and extremely young. Married people made the difference.) Gays and lesbians didn't switch votes as groups (they were already solidly backing the Dems). Straights did.
6. Voters who think the economy is okay (good and not good, but not excellent or poor) switched votes and gave the triumph to the Dems. By far. Actually, people depressed by the state of the economy switched from Dem to Rep! Same those who believe that the economy is in excellent shape! Not that it mattered, but it is interesting to note.
7. Small city dwellers and suburbanites made the difference. Small towners and rural folks switched votes the right way, but didn't make much of a dent due to being only 23% of all voters. By region, most people switching votes, were in the Northeast and West, where the Dems were already stronger. But the Midwest and South did switch votes, and in the right direction, but the size of the shift altogether was smallish compared to that in the other 2 regions.