On Friday the Daily Mail reported that Tory MPs plotting against the leadership intend to send a letter to the prime minister calling on him to sack the chancellor if the economy fails to improve after the Budget in March.
Asked whether Cameron had confidence in Osborne, a Downing Street spokeswoman told reporters: "Yes ... the Prime Minister has full confidence in the chancellor."
She added: "We have a plan to deal with a record deficit and we are sticking to that plan."
And according to The Guardian, Cameron risks facing a insurrection against his leadership in the summer of 2014 if he fails to improve his party's poll rating.
The paper reports that enough MPs are believed to be prepared to trigger a vote of no confidence in the prime minister if he does not start to do better.
Under Conservative Party rules a leadership contest is triggered if 46 MPs sign letters calling for a vote. It is believed some of Cameron's harshest critics have already submitted their own letters.
The rumours of plots emerged after little known backbencher Adam Afriyie was accused of running a not-so-secretive campaign to succeed Cameron should the Tories lose the election in 2015.
Cameron made fun of the stories during prime minister's question time on Wednesday, when a Labour MP asked if there were "traces of stalking horse" in the Conservative Party.