Up-and-climbing socialite Olivia Palermo may still be smarting from her feud with rival Tinsley Mortimer, as “Page Six” reports today, but she’s got bigger problems, ones that have million-dollar price tags. Palermo’s pop and personal slush fund, real-estate consultant Douglas Palermo, recently lost a hefty bankruptcy case. Palermo senior’s appeal to get out of paying over $2.75 million to a creditor was rejected after the judge found that Palermo had used multiple fake organizations to obscure his actual worth from lenders. Instead of paying his bills, Palermo joined private clubs and sent his children, Olivia and Grant, to expensive schools. He also issued “hundreds of checks” to his Korean dry cleaner, which he used as an “unofficial credit line,” and skimped on alimony payments. That’s gotta sting for flashbulb-friendly Olivia — if dad’s in debt, does daughter have to … work?