The Conservative Party leader told Sky News the general election needed to deliver a strong government capable of making long-term decisions.
A YouGov poll for the Sunday Times has suggested a widening lead for the Tories but Mr Cameron acknowledged the result would be “tight”.
He insisted an overall Conservative majority was still “do-able”, adding: “That is what I am shooting for.”
He would not be drawn on the possibility of a post-election pact with the Liberal Democrats if there was a hung parliament, under which no party has an overall majority.
“I am hoping to win the election outright. I think that is absolutely do-able and deliverable,” he told the channels’s Sunday Live with Adam Boulton.
“It is a challenge, it is a tight election, it is going to be very close.
“We are fighting for an overall majority, we think that would be best for Britain. We think a hung parliament would be damaging, the uncertainty would be bad for Britain.”
He went on to defend Tory plans to reverse part of the government’s planned increase in National Insurance (NI) contributions.
Labour has claimed the Conservative plan could only be funded with a rise in VAT, which the Tories deny.
On Sunday, Schools Secretary Ed Balls said the Conservatives would raise VAT “within weeks” if they won power in the election, expected on 6 May.
Mr Balls told the Observer shadow chancellor George Osborne would be unable to fund tax-cutting promises, including the NI pledge, without a VAT increase.
“They will do it within weeks. We don’t need to because we have set out our deficit reduction plan for four years which does not involve raising VAT,” Mr Balls told the paper.
Business Secretary Lord Mandelson joined the debate in an interview with Sky’s Sunday Live programme.
He suggested the standard rate of VAT – currently 17.5% – would have to rise to at least 20% in order to make up the lost revenues.
But last week David Cameron denied he was planning to raise the purchase tax. The party has said it will pay for the tax pledge by cutting about £6bn in government waste and bureaucracy in 2010-11.
Tory advantage doubled
Lord Mandelson also said in the Sky interview that Labour remained the party of business.
He said they had been elected as a “pro-business and pro-enterprise party” and would remain so.
“We’ve just produced a budget for business that doubled their investment allowances, doubled the relief for entrepreneurs who start and grow businesses, we’ve put in place new funding for small and medium-sized enterprises, and we’ve introduced measures too that in time are going to get the banks lending more,” he said.
Earlier this week 37 business leaders, from companies including Marks and Spencer and Diageo, signed open letters backing the Conservatives’ plans to cancel part of the planned rise in NI contributions.
A YouGov poll in the Sunday Times has suggested the Tories have doubled their advantage to 10 points compared with last week.
The results put the party up two on 39%, Labour down three on 29% and Liberal Democrats up one on 20%.
YouGov interviewed 1,503 voters online on 1 and 2 April.