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On the morning after Barack Obama’s historic nomination victory, attention has quickly turned to the question of possible running mates — specifically whether Obama and Hillary Clinton will join forces in a so-called “Dream Ticket.”

In a survey conducted in late May (May 21-25), a majority of Democratic and Democratic-leaning voters (53%) said they would like to see Obama choose Clinton as his running mate. However, Obama supporters viewed a possible Obama-Clinton pairing as anything but a dream. Fully 54% said they did not want to see Obama choose Clinton as his running mate while 37% said they did. Clinton supporters, not surprisingly, were much more open to the idea — 76% said they would like to see Obama to choose Clinton as his running mate.

An analysis of the data finds that, despite the sharp differences between Obama and Clinton supporters on this issue, key Democratic voter groups — including some that have consistently supported Obama for the nomination — have a positive view of a possible Obama-Clinton ticket.

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For instance, black voters supported Obama over Clinton for the nomination by 80% to 15% in Pew Research’s May survey. Most black Democrats (59%) say they would like to see Obama choose Clinton as his running mate. About the same proportion of liberal Democratic voters (58%) — who also supported Obama for the nomination by wide margins (61% to 36% in May) — express a positive opinion of a possible Obama-Clinton pairing.

However, college-educated Democrats, who favored Obama by 25 points over Clinton in the May survey (60% to 35%), are evenly split over whether Obama should select Clinton as his running mate: 46% say he should not, while 42% believe he should.

The prospect of Clinton taking the number two slot on the ticket attracts broad support from groups that have long favored her candidacy — less educated Democrats and women. Nearly two-thirds of Democratic voters (64%) with no more than a high school education say that Obama should choose Clinton, as do 59% of women.

Find more from Pew Research’s latest national political survey at pewresearch.org/politics.