I would say it depends on your definition of "promiscuity". The basic definition is just casual sex with multiple partners (such as a one night stand). I wouldn't say that's the "norm" so much as it's something that has been both glorified (in an attempt to empower women, mostly) and shamed (in an attempt to reinforce masculine dominance and/or religious beliefs) in the media in order to gain a certain amount of shock factor.
But if you mean (as my grandparents do) the fact that people have sex within the confines of committed relationships (though they aren't married), then I would say yes, that's most likely the "norm". I wouldn't necessarily say it's "new" however.
The notion of multiple sexual partners has been around in human society since the beginning. Mistresses were commonplace (and far from frowned upon) up until recent centuries (take for example, Madame de Pompadour, the "uncrowned queen of France" and Louis XV's mistress). It was typical for men to have multiple sexual partners and there was nothing wrong with it (the only reason it was frowned upon for women to do so was because it would pollute the family line and tamper with family heirs, etc).