The Conservatives need 23 seats more than they won at the 2010 election to secure a majority in the House of Commons.
Mr Cameron said a Conservative government would ensure "British people will have security at every stage of their lives".
"If Britain delivers a Conservative government, I make this promise: Britain will continue on the road to a brighter future. Our policies will deliver more childcare and jobs, help people buy their homes, cut taxes, and give people the retirement deserve," he said.
"A vote for UKIP or the Lib Dems opens the back door to a Labour government: It will result in Ed Miliband as prime minister, unable to survive without SNP support. And that support will cost you money. They will take us back to square one, with heavy borrowing and higher taxes for more welfare. An economy facing ruin."
Speaking to BBC Radio 4's Today programme from Wales, Mr Cameron said he was still "fighting" to win enough seats to form a government on his own - and would continue to talk about policies until the polls closed.
"People still have the chance to shape the election with their vote and we can achieve an overall majority that gives Britain the strong stable government that continues with a long-term economic plan that is working: the jobs, the growth, the houses we want to build, the childcare we want to provide, the good retirement we want to provide for our people - those things are in reach," he said.
Asked about the SNP, Mr Cameron insisted he had "every right to warn of the dangers of a bunch of nationalists who don't want our country to succeed".
He said if there was no clear winner after Thursday's poll, people only needed to look at what happened in 2010.
"I formed the first coalition government for 70 years because I wanted to provide strong and stable government for Britain," he said.
"I will always put the country first and always do what I can to provide that strong and stable government."
The prime minister was also asked about a Daily Mirror report that claimed former Prime Minister Sir John Major had said Britain must "acknowledge the fact we have a pretty substantial underclass".
"There are parts of our country where we have people who have not worked for two generations and whose children do not expect to work," Sir John is reported as saying.
Mr Cameron said Sir John was "absolutely right to make these points".
He said he was not satisfied with the situation and that was why he wanted another five years in office to follow through on reforms to welfare and education.