"Anyone claiming that America's economy is in decline is peddling fiction."
"Peddle" in this context means to spread, and "fiction" is that which is invented or made up. (See http://dictionary.cambridge.org/dictionary/english/peddle and http://dictionary.cambridge.org/dictionary/english/fiction)
So "peddle fiction" means to spread rumours or lies, and the implication is that the people doing this are doing so wilfully.
One definition of the word 'peddle' is to sell something, and the seller, a 'peddler', was traditionally a person who travelled from village to village, selling, or peddling goods.
In this case, the expression is used somewhat idiomatically. What the author is trying to say here is that anybody who claimed that the economy of the USA was in decline, is 'selling' untruths to people - in other words, lying.