If the critic's name has more kudos than the newspaper then credit the critic. If not, use the newspaper. There's nothing wrong with "Leslie Wright of Blogcritics.org said" , especially if you're wanting Leslie to review your next book ;-)), but I would think the newspaper will carry more weight with prospective readers.
One way round your problem would be to quote part of the review (most reviews are far too long for quoting in full) credited to the blog, and then another part credited to the newspaper. Quite often, what you read on a book jacket isn't actually what the review meant, but by taking words out of context, they can be spun.
By the way, a review isn't a blurb. A review is someone's opinion. A blurb is technically a teaser as opposed to a synopsis which tells you what happens in the story - not good to put in a blurb!
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