In a broadcast speech that included a call for the Scottish to remain a part of the UK, the Prime Minister said the Government would "redouble" efforts he claimed were "turning the country around".
"We're going to keep on doing everything possible to help hardworking people feel financially secure," he added.
Westminster Advisers MD Dominic Church said the speech was part of a recent drive to make Cameron "a bit more human in the way he talks about everyday concerns".
The speech followed a change in rhetoric evident in the final PMQs of 2013, Church said, in which the focus was less on economic figures and more on "people and their situations".
"It was well delivered, if slightly patronising, and is about showing he has a more caring side," Church added.
"This is an attempt to outflank [Labour party leader] Ed Miliband’s message, which is all about living standards and relieving the pain."
Speaking ahead of their referendum on independence in September, Cameron told the Scottish public: "We want you to stay."
Other priorities highlighted by the Prime Minister for 2014 included further moves to cut immigration and the welfare bill, as well as driving up school standards.
Cameron also reflected this focus in an editorial piece for The Times yesterday, in which he said that Britain would start turning into a "post-Great recession success story".
In his own New Year's message, Ed Miliband pledged to tackle "the biggest cost of living crisis in a generation".
Deputy Prime Minister Nick Clegg, meanwhile, told voters the Liberal Democrats were "Britain's party of in" regarding the European Union.