DISCLAIMER: I am in no way a professional statistician, and this should not be considered any sort of definitive mathematical analysis. It is more just a sort of thought experiment based on the 2008 and 2010 exit polling data and some rough number-crunching with my trusty Excel spreadsheets.
Anyway, what I decided to do, in a nutshell, was try to calculate what the results in the Senate, and in some key House races, might have been if the electorate had turned up to vote in the percentages reflected in the 2008 exit polls, but the various subgroups (e.g. liberals, moderates, and conservatives, or Obama & McCain voters) had still voted either Democratic or Republican in the percentages reported in the 2010 exit polls.
For example, suppose a state went 55-45 for Obama in 2008, and in that same state's Senate race in 2010, the exit polls indicated that Obama voters voted Democratic 85-15, and McCain voters voted Republican 90-10. So the projected result, if the 2008 electorate had turned up, would be as follows:
Democratic: (55% x 85%) + (45% x 10%) = 46.75% + 4.5% = 51.25%
Republican: (55% x 15%) + (45% x 90%) = 8.25% + 40.5% = 48.75%
I ran these calculations for three different breakdowns: party ID (Democratic, Republican, or Independent); ideology (liberal, moderate, conservative); and 2008 presidential vote (Obama, McCain). Obviously, there is going to be some variation in how people identify themselves from one election to another, and even in the presidential vote breakdown, people may, for one reason or another, give an incorrect answer to an exit poll. Plus, of course, there is no guarantee that, for example, all the moderates from 2008 who didn't show up in 2010 would have divided their votes the same way as the moderates who did show up in 2010. As I said, this is more just a "what if" than a solid mathematical analysis.
This ended up getting pretty detailed, so rather than post everything at once, I'll break it up over several diaries, and continue partly based on whether or not anyone finds it interesting. Below is a screencap from Excel, displaying the results for 19 Senate races: for each race, the actual results are listed first, followed by the projected results if the turnout had matched the 2008 exit poll responses for party ID, then for ideology, and then finally if the Obama/McCain breakdown had matched the actual 2008 outcome. After the screencap are some brief commments on some of the races.
ARKANSAS (Boozman (R) def. Lincoln (D) 58-37)
This was one case where there doesn't appear to be that much difference between a hypothetical 2008 electorate turning up and the actual electorate that turned up in 2010. If the liberal/moderate/conservative split had matched 2008, then Lincoln would have been a little closer (56-40), but it's still not really anything to write home about, and the projections based on partisan ID and presidential vote match the 58-37 result that we got on Election Night.
COLORADO (Bennett (D) def. Buck (R) 48-47)
This is the one instance I've found so far in which a Democratic win could have turned into a Republican win if the electorate had resembled one of the 2008 exit poll breakdowns, in this case the division by party ID. Strangely enough, the partisan breakdown in CO appears to have gone from a 1-point Democratic deficit in 2008 (30D/31R/39I) to a 5-point Democratic advantage in 2010 (33D/28R/39I). It's certainly tempting to just dismiss this out of hand - it is difficult to imagine any Democrat who survived 2010 losing at the hands of 2008's voters. On the other hand, if there were a combination of (a) high GOP "crossover" to Obama in 2009 and (b) low GOP turnout in 2010, then I suppose this could be for real, and certainly Colorado Republicans had cause to be disillusioned over the mess on the gubernatorial side. I also wonder, however, if perhaps some conservative voters were, by the simple act of voting for Tancredo for Governor, led to identify themselves as Independents when they might have called themselves Republicans in the context of a traditional 2-party race. In any case, the projections based on 2008 ideology and presidential vote both show Bennet winning by a larger margin than he actually did.
ILLINOIS (Kirk (R) def. Giannoulias (D) 48-46)
All three projections - those based on party ID, ideology, and 2008 presidential vote - suggest a Democratic victory if the electorate had resembled its 2008 composition. Obviously, 2008 may have been something of a high-water mark for Democrats in Illinois given the "favorite son" aspect working in Obama's favor. Still, any way you slice this, the numbers indicate that a turnout closer to 2008's could have turned this narrow Republican win into a narrow Democratic win.
Given Illinois's reputation as a fairly solid blue state, I also looked at the 2010 crosstabs for indicators of "defections" from those who might be expected to vote Democratic. According to the 2010 exit polls, Giannoulias held onto 86% of Democrats and 87% of liberals, but only 78% of Obama voters. He also won only 51% of moderates (compared to 55% of moderates who voted Democratic in the House exit poll), and got absolutely pasted among Independents (28-61) - presumably these Independents were a substantial portion of the defecting Obama voters. Even his percentages among Democrats and liberals were below those two groups' Democratic-voting percentages in the House exit poll, for that matter.
INDIANA (Coats (R) def. Ellsworth (D) 55-40)
It may be that this seat was a goner without Evan Bayh running again, but there was one scenario in which it would have at least been close. Indiana voted 50-49 for Obama in 2008, but the electorate that turned up in 2010 was 51-41 in favor of McCain. My projection estimates that a turnout resembling 2008's presidential vote would have resulted in just a 4-point victory for Coats.
KENTUCKY (Paul (R) def. Conway (D) 56-44)
While the projections based on 2008's ideological composition and presidential vote don't show this one especially close, a partisan breakdown equal to 2008 estimates that Paul would have won by just 3 points, 51-48. In 2008, the partisan breakdown in the exit poll for Kentucky was 47D/38R/15I, but in 2010, it was 38D/40R/22I. Given the discrepancy, it seems possible that this was not entirely a shift in turnout, but also a segment of Kentucky voters simply being less likely to call themselves Democrats in 2010 than in 2008.
MISSOURI (Blunt (R) def. Carnahan (D) 54-41)
This was tagged as a competitive race early on but eventually slipped away from the Dems. The projections based on partisan ID and presidential vote do at least suggest a close race - about a 5-point GOP win - if the electorate had resembled 2008's, while the projections based on ideology still have Blunt winning by about 10 points. The 2010 exit poll does show Carnahan underperforming, relative to the breakdown in the House vote, among both liberals (82%) and moderates (52%).
NEVADA (Reid (D) def. Angle (R) 50-45)
The 2010 exit poll data do seem to back up the notion that Reid won in part because Angle was seen as too extreme. In the House, Independents voted 56-37 for the Republicans, but in Nevada Angle carried Independents by just four points, 48-44. Reid also won 65-31 among moderates, compared to the 55-41 split in the House poll. Interestingly, Reid also showed above-average support from those we might normally consider the base Republican vote. In the House poll, self-identified Republicans voted 94-5 GOP, self-identified conservatives voted 84-13 GOP, and McCain voters voted 91-7 GOP. In Nevada, Angle's numbers were 85-11 among Republicans, 78-17 among conservatives, and 86-10 among McCain voters.
So...that's all for now, but as I said, I'll continue this for the rest of the Senate and for the House if people are interested.