Several people who signed the petition on website Petition Online claimed they were unable to get through to vote for White.
Ian Bagley called the show a "total fix" after he said he was unable to phone through.
Another petitioner, Chantelle, said she received a "dead line" when she tried to call.
However, an X Factor spokeswoman said there were "absolutely no issues with the phone lines".
She added: "Our viewers vote for the act they want to keep in the competition and last Saturday, Laura White and Ruth Lorenzo received the least number of votes."
Culture Secretary Andy Burnham on 'the wonderful and talented' Laura White
Similar fan protests were seen last year after Welsh singer Rhydian Roberts was voted off the contest - with media watchdog Ofcom receiving as many as 1,500 complaints.
In the petition, some of White's supporters also accused X Factor judge Louis Walsh - who had the casting vote - of getting rid of the singer so that his group, JLS, would have a better chance of winning.
One fan, Donna Clarkson, said the result was an "absolute joke" and suggested Walsh should have "let it go to deadlock".
In that situation, the singer with the lowest support from the show's phone vote would have been sent home.
When contacted by BBC News, Walsh declined to comment on Saturday's decision.
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