Normally I'd use the latest Survey USA poll, due to their accuracy so far this year (with notable exceptions in Southern states and Missouri), but their latest April 15 poll was Clinton 62%, Obama 26%, a gap of 36 points.  I have trouble believing that poll is anything but a massive outlier.  The poll has Clinton getting 23% of the African-American vote, as well as winning 18-34 year olds  by 60%-31%.

Survey USA is often held up as a beacon of accuracy, but they have a tendency, noticed by others as well as by me, to drop big outliers weeks before a contest, only to suddenly fall in line for their last poll.  They did this in Ohio (putting her up by 20% until the last week) and in Pennsylvania (putting her up by 18% a week out).  I would be surprised if Survey USA's last Kentucky poll shows anything greater than a 20% split.

Survey USA's previous Kentucky poll on March 31 found Clinton ahead of Obama 58% to 29%, a gap of 29 points.  This one has more believable breakdowns, and I'm going to go with these assumptions for my breakdown, although Clinton may very well get close to 70% as their last poll indicates.

For the purposes of this prediction, I will guess Clinton wins 65%-35%, in keeping with SUSA's first poll if they split undecideds.

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The PLEO delegates will split 4-2 for Clinton as long as she clears 58.3%, but she won't get any more unless she crosses 75%, which ain't happening.

The At-Large delegates will split 7-4 as long as Clinton passes 59%, but she can't get any more unless she breaks 68%.

Subtotal: 11-6 statewide.

Then it's on to the district delegates.

KY-01: 5 delegates.
Represented by Republican Ed Whitfield, this district encompasses the western side of the state, bordering rural counties in Tennessee, Missouri, Illinois, and Indiana.  Obama will get stomped here, but will Clinton get above 70%?  It's possible, and unfortunately I think likely given the Survey USA polls, though I would love to be proven wrong.  4-1 Clinton.

KY-02: 5 delegates.
Represented by retiring Republican Ron Lewis, a rural district just south of Indiana.  Same dynamics here, can Obama avoid falling below 30%?  Until polling shows otherwise, this one is 4-1 Clinton.

KY-03: 8 delegates.
Represented by Democrat John Yarmuth, who has endorsed Obama in February, this is an urban district surrounding Louisville.  Will Obama be able to win this district?  I guess the question we should be asking (if we are accepting that Obama faces a 65-35% loss statewide) is can Obama avoid a 3-5 loss?  Whoever gets above 56.25% gets the extra delegate.  If Obama improves his standing in this state that shouldn't be a problem given the nature of this district.  However, if he's getting rolled over statewide he probably is lucky to just hold Clinton under that number.  4-4 for now.

KY-04: 5 delegates.
Represented by Republican Geoff Davis, this district is located in Northern Kentucky and borders the rural Ohio districts that gave Clinton over 70% of the vote.  Unless SUSA is way off the mark, he doesn't avoid that here.  4-1 Clinton.

KY-05: 5 delegates.
Represented by Republican Hal Rogers, this district takes in Eastern Kentucky and borders rural districts in Tennessee and Virginia that gave Clinton almost 90% of the vote.  Obama just needs to maintain viability (15%).  4-1 Clinton.

KY-06: 6 delegates.
Represented by Democrat Ben Chandler, this central district includes the cities of Lexington and state capitol Frankfurt.  Clinton will need 75% of the vote to get five delegates here, which I don't think she will manage given the cities here.  4-2 Clinton.

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All together that's 35-16, a nasty loss for Obama that certainly won't be canceled out by Oregon, and one that would give her more net delegates than any state since Super Tuesday (only Arkansas, New York, and California have given her more).

However, I am confident that once Obama campaigns here his numbers will improve, and he will at least hold Clinton to 61 or 62%.  Just by doing that he will decrease the delegate loss substantially, reducing districts KY-01, KY-02, and KY-04 to 2-3 losses, and possibly winning KY-03 by 5-3.  if he can do that then the delegate count changes to 30-21, a much more palatable loss.