A poll by SES Research gave the Conservatives 33 percent support, down from 36 percent on election night, and now tied with the opposition Liberals who were ousted over corruption allegations.
"The Conservative governments honeymoon was short-lived," Nikita Nanos, president of SES Research, said in a statement.
The Liberals vowed to defeat the government, despite significant debts and a leadership void since former Prime Minister Paul Martin resigned after losing the January 23 election.
But, the separatist Bloc Quebecois said it would prop up the Conservative government of Prime Minister Stephen Harper for now.
The Conservatives hold 125 seats in the 308-seat House of Commons.
With the help of 51 Bloc Quebecois MPs, they can effectively prevent the Liberals, who have 102 seats, from defeating the government.
The New Democratic Party has 29 seats and there is one independent MP.
Cabinet controversy
Meanwhile, a controversy over two cabinet appointments lingers and the Ottawa press pool recently filed an unprecedented formal complaint with the prime minister's office over being shut out by Mr Harper and his ministers.
Mr Harper replaced his communications director this week.
"I will be available whenever I have something to announce," Harper said on Tuesday.
But criticism over his appointment of a former star Liberal minister, who defected from the Liberal Party just days after the election, and an unelected party organiser to his cabinet still dog Mr Harper's government.
The Conservatives won the January 23 election largely on a promise to clean up government after 12 years of scandal-tainted Liberal rule.
Party organiser Michael Fortier is now responsible for billions of dollars in government spending as publics works minister.
David Emerson, previously a star minister in Paul Martin's Liberal government, is the new Conservative trade minister.
Mr Harper appointed Mr Fortier to the Senate to make the cabinet posting more palatable, but that too sparked outrage since Mr Harper had campaigned for an elected Senate.
Currently, senators are appointed by the governor general on the advice of the prime minister, but scores of Canadians have demanded Senate reform.
The SES survey of 1,000 people was conducted from February 4 to 9, days after Harper's government was sworn in, and has a margin of error of 3.1 percentage points.