The Clinton campaign yesterday released a PowerPoint presentation that trumpets their candidate's performance in so-called "tough" districts. These are districts with a freshman Democratic member of Congress but that voted for Bush in 2004. The PowerPoint calculates that Clinton has won 16 of 20 such districts.
Naturally, I've decided to take a somewhat more comprehensive look at this question. Below is a table containing all House, Senate and gubernatorial races that are presently rated as competitive by the Cook Political Report. Clinton does indeed have a 40-31 lead in competitive House districts. In many of these districts, her wins have been by impressive margins (although the same is true of many of Obama's districts). However, Obama leads 8-2 in states with competitive Senate races, and 5-1 in states with competitive gubernatorial races. If the three types of races are combined, Obama has a tiny, 44-43 edge over Clinton. In races that are classified as "highly competitive" (toss-ups or leaners), Obama's lead is 29-27, though Clinton maintains a 24-21 edge in highly competitive House races.
(Notes: States marked with an asterisk have not compiled their primary or caucus returns by Congressional District. In these instances, the winner of the district was inferred from county-level results. Also, I am not counting Michigan districts toward the totals, although I am counting Florida.)
One other issue is that it does not necessarily follow that the candidate that won a district would necessarily have longer coattails there. Obama's primary electoral weakness is that a relatively large number of Democratic voters presently claim that they'd defect to vote for John McCain in an Obama-McCain matchup. However, if these crossover Democrats are splitting their tickets, this would not necessarily hurt the downballot candidates. Clinton's primary electoral weakness (given the ways that she might win the nomination at this stage) is that she might depress turnout among Democratic-leaning voting groups like black voters and young voters. If these voters do not turn out, they will not be able to cast a ballot for the Democrat in downballot races.
A related question is whom the legislators and executives in competitive districts have chosen to endorse. That tally is below. Note that since most of the competitive districts this cycle are held by Republican incumbents, there was no endorsement available in many cases. I also do not list an endorsement where the Democratic incumbent is retiring.
Obama leads Clinton 14-8 in endorsements from competitive districts, including an 12-7 edge in House races. (EDIT - Have now added Obama's new endorsement today in AZ-5). Three sitting Democratic congressmen in competitive districts (PA-8, NH-1 and IN-9) have endorsed Obama even though Clinton carried their district. None have crossed over to endorse Clinton in an Obama-won district. If these legislators are behaving self-interestedly, they may evidently believe that Obama will carry longer coattails for them than Clinton.