Simon Danczuk, the MP for Rochdale, also took a swipe at the Conservative's repeated use of the phrase "hardworking people".
The public no longer responded to the kind of simple political messaging successfully employed by Tony Blair and Peter Mandelson, Mr Danczuk said.
But Labour insisted it would continue to use "One Nation", as party sources pointed to the successes of the party's sloganeering.
Last month Lib Dem business minister Jo Swinson appeared to accept Labour's charge that there was a "cost of living crisis" when she used the phrase in Commons.
A Scottish Labour source also said: "It worked for Harold Macmillan and it will work for us. It's also handy to remind the SNP that we are 'One Nation'".
Mr Danczuk had earlier praised his leader's "One Nation" party conference speech two years ago, as a "land grab moment".
But, he added: "It's not a general election winning strapline is it? The public isn't as accepting of such simple messaging any more.
"Indeed, I've come to believe the public is actively turned off by the torturous repetition of political mantras."
Instead, he highlighted the success of outspoken Labour politicians such as Glasgow MP Tom Harris.
"The premium currency that politicians should be looking to trade in these days is authenticity, and that means using stories and experiences to convey the message, not parroting slogans," he said.
Conservative MP Stewart Jackson said:"This vacuous slogan belies Labour's core philosophy of more spending, more borrowing and more taxes."