Mr Cameron is currently half way around the world on a visit to Amritsar, in India, on a UK trade mission.
But he told reporters: “We’re fighting a very strong campaign. It’s up to the people of Eastleigh.
“I think if they vote on the best candidate, who backs my plan to sort out Britain’s deficit, get Britain moving, have a proper reform of welfare, proper immigration policies; those plans and Maria, as the candidate, are what people should vote for.”
Last week the Prime Minister visited the constituency last week in a bid to drum up support for the Conservative candidate.
He addressed hundreds of employees at B&Q on Valentines Day, before joining Mrs Hutchings canvassing for voters on the streets.