I shall begin with a number of premises:
1. No policy foundation is perfect. No matter how perfect it may seem in theory, it won't work perfectly in practice and will always give rise to undesirable consequences.
2. Opposition to a policy foundation will form. This may be immediate, or it may be subsequent to the aforementioned undesirable consequences arising.
3. Those who oppose a particular policy foundation will always focus on the undesirable consequences in an attempt to sway public opinion to their way of thinking.
4. Eventually those who oppose the policy foundation will garner enough public support that there will be a strong shift away from the policy foundation to a new policy foundation that has been built upon by those who opposed the previous.
5. Just before the strong shift occurs, there may be a strong result in the opposite direction. This is because the opposition to the current policy foundation almost reaches the tipping point and those put forward a candidate who focuses on their alternative foundation. Because the opposition does not yet have enough support, they don't win, however the public that is completely satisfied with the status quo responds strongly to the opposition canddiate.
At the point where the public shifts from one policy foundation to another is the realignment. Because of the nature of elections, there will be a point at which the scales tip, but it may take a few years for them to tip completely (maybe three midterms?).
When this occurs, the party that dominated the previous policy foundation will do some soul searching and will be forced to re-invent itself with new candidates predominantly holding positions closer to where the lines are drawn with the realignment (for example, more conservative democrats or more liberal republicans).
I don't know if I have put that particularly clearly - I'm trying to say that opposition to a fundamental idea (not a single policy, but the foundation that links many policies) gradually rises. This might be military intervention (as opposed to the War in Iraq, which is a single policy only). It might be christian conservatism (as opposed to individual issues of abortion or gay marriage).
For this reason, I think any realignment would be more likely to be to the left rather than the right - although as JJ says, it could be leftish in some aspects and rightish in others.
Like JJ, I think a realignment is forming. When people are calling for change, and not just a new ideas, but a change in how things are actually done, it looks like people are ready to shift from one foundation to another. Also like JJ, I'm not sure what it's going to end up looking like, but I think it would probably typically be considered a shift to the left with more liberal democrats and more moderate republicans.
I'm not sure exactly what policies will be affected or what foundation specifically will be shifted, but my guess is that it's happening more in response to the War in Iraq being a crystalising issue showing perceived failures in a policy platform of overseas military intervention. I think that it will result in the US becoming somewhat more isolationist, a decrease in military spending, and a greater focus on US domestic issues such as health and education.
I think that this issue is the one that's most going to change, because the timing feels about right. Reagan increased military spending and there has been US intervention in Somalia and the Balkans before Iraq, Iraq is the tipping point where it hasn't been an immediate success in the eyes of the public and has been the issue that opponents of military intervention have been able to focus on (point 3 of my initial premises). As the 2006 mid-terms swung heavily against the Republicans as a backlash against the War in Iraq, I think that's the direction public opinion is heading.
Now... this is a long call to make, but I think that if this is the case, Indiana going to be a surprise state in November. It has over 100 casualties in Iraq (see
http://projects.washingtonpost.com/fallen/states/ ) and had seats changing hands in 2006. I'm still doing some analysis on swings in the state there over the past few elections, but I think that it's going to either be quite close - and maybe even go dem for the first time in goodness knows how long.
In 2004, Bush received 60% of the vote to Kerry's 39% (I haven't looked at Congress figures yet). In 2006, Republican Congressional candidates received 49.90% of the vote to the Democrat Congressional candidates' 48.74%. I know that I've compared two different races, but I will do the 2004 Congressional figures shortly and update those figures.