Hotfoot from his job as Canada's central bank boss, he must conjur sustained and strong growth from an economy that remains highly indebted, and is suffering from a lopsided recovery that favours services over manufacturing while the government prefers to hack at public spending with little thought for its long term impact while waiting for something to turn up.
George Osborne wants the central bank to take the lead and lubricate the financial system with so much money that banks start lending to small businesses again. Carney, by all accounts wants to fulfil the chancellor's dreams.
But will Carney match his undoubted finance skills with a magician's ability to turn rabbits into doves, or will the former Goldman Sachs banker find himself, like the Wizard of Oz, furiously pulling levers to no great effect?
There are many observers who believe his job is more constrained than when he accepted Osborne's invitation last year to succeed Sir Mervyn King.
The economy is growing, and while any recovery may still be fitful and fragile, it is enough for a majority of members of the monetary policy committee (MPC) to resist pumping in further cheap funds.
Inflation remains above 2% and looks like staying above the target set by the government for several years.
Martin Weale, the former head of the National Institute for Economic and Social Research (NIESR) and a long-standing MPC member said last week that he had blocked pumping further central bank funds into the financial system because he feared it would push inflation higher.
A further modification of the MPC's remit could persuade Weale and the others to relax about inflation and agree to what until now would have been considered wild and reckless policies. The MPC has created £375bn of funds under its quantitative easing programme and could create much more. Three members of the committee, including King, have pushed for a £25bn hike.
Carney could also ask the committee to buy the high street banks' toxic debts, which are preventing them from meeting regulatory rules on having clean and detoxified reserves. He might not buy the worst stuff on the books of RBS and Lloyds, but he would only be following the US Federal Reserve if he found himself with several hundred millions pounds' worth of mortgage debt on the BoE's books.
He could support an investment bank with central bank funds, as the British Chambers of Commerce have urged him to do, or set up an offshoot of the MPC to consider direct investment in house building through the bond market, as the New Economics foundation has requested.
One of his most likely projects will be to persuade the MPC to back a commitment that interest rates stay low until a target on unemployment or growth is reached, much as the Fed has done. The aim would be to free consumers from the worry of rising rates and encourage them to buy something they have resisted purchasing, maybe a sofa, a car or even a house.
Even if he is minded to take on the task of supporting a £1bn investment bank and pumping countless millions into housebuilding, or providing some notice on the next interest rate rise, he faces several barriers.
First there are the critics of the BoE's current policy, who say the UK's situation is better than supposed and in need of rate rises. According to monetarist economists, GDP growth so far this year is a sure sign that the economy is already back on track for good.
Simon Ward, the chief economist at the fund manager Henderson Global Investors, reckons growth this year will be 2% and not the less than 1% predicted by mainstrean forecasters and the BoE.
He said the demand for cash in instant deposit accounts, known as narrow money or M1, had surged since last summer, a situation ignored by the Bank of England.
Arguably, much of the boost to spending in the last couple of years is a direct result of the PPI scandal, which has forced banks to pay compensation in the region of £5bn and employ thousands of staff to handle the mess, also at a cost of more than £5bn. Households and smaller companies also remain hugely indebted, placing a further drag on confidence and spending.
If he can paint a gloomier picture of the economy and bypass his monetarist critics, there are six of the nine MPC members standing in his way. They may not be monetarists, but they remain wedded to the idea that the economy is finely balanced and that a wait-and-see policy is needed.
Should they acquiesce, there would be another problem, in that monetary policy has not been the panacea some had hoped for.
King championed a lower exchange rate. He said that devaluing the currency through printing extra sterling would help exporters and rebalance the economy.
It's true that UK defence exports totalled £8.8bn over the past year, a rise of 62% from 2011 and making Britain the second largest defence exporter after the US. Car exports are also up, transforming a £7.5bn deficit in car exports in 2003 to break-even. Exports to emerging countries from Brazil to Indonesia are inching higher. But our biggest market, the EU, is in the doldrums and looks likely to be stuck in a cycle of low growth for some time. The BoE also seems to have underestimated the extent to which exporters are wrapped into long-term fixed contracts that are hedged against currency movements. In short, it takes a long time for the exporting supertanker to turn.
Banks are supposed to benefit from QE, which involves them selling their government debt to the BoE at a profit and then investing the money in small businesses or at least increasing their borrowing limit. As Tory MP Jesse Norman was at pains to point out last week, however, lending to small businesses has declined.
Banks have limited their loans to big business and affluent households in search of cheaper mortgages, giving us some very profitable FTSE 350 companies and spiralling house prices in the south-east. Banker bonuses are on the rise and as Income Data Services points out, boardroom director bonuses have soared over the last year by 17% to 38% of pay. Banker bonuses are also back in vogue as an oligopoly of lenders that dominate the sector reward themselves accordingly.
Jim Leaviss, who manages £30bn worth of bonds on behalf of M&G investors, is concerned that Osborne's determination for Carney to follow the Federal Reserve with forward guidance can only lead to worse behaviour by spivvier parts of the City. Telling them that interest rates will stay low for longer will only spur wilder and riskier investment strategies. Leaviss wears a worried frown when he talks about the City's drift towards old excesses.
Investors want to earn a high rate of return and if that means reinventing some of the more exotic derivatives so popular before the 2008 crash to make money, then so be it. Such a tactic would never win Carney's endorsement, but he may just be the marketing man that the worst spivs in the City have been looking for.
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