To critics, it is a Hail Mary play — an admission that the economy’s persistent weakness has all but exhausted the central bank’s powers and tested the limits of its policy making. Around the world, some warn the unusual strategy will weaken the dollar and lead to crippling inflation.

But inside the Operations Room, on the ninth floor of the New York Fed’s fortresslike headquarters, there is no time for second-guessing. Here the second round of what is known as quantitative easing — QE2, as it is called on Wall Street — is being put into practice almost daily by the central bank’s powerful New York arm.

Each morning Mr. Frost and his team face a formidable task: they must try to buy Treasuries at the best possible price from the savviest bond traders in the business.

The smallest miscalculation, a few one-hundredths of a percentage point here or there, could unsettle the markets and cost taxpayers dearly. It could also embolden critics at home and abroad who say QE2 represents a dangerous expansion of the Fed’s role in the markets.

“We are looking to get the best price we can for the taxpayer,” said Mr. Frost, a buttoned-down 34-year-old in a striped suit and rimless glasses.

Whether Mr. Frost will reach that goal is uncertain. What is sure is that market interest rates have risen, rather than fallen, since the Fed embarked on the program in November. That is the opposite of what was supposed to happen, although rates might have been even higher without the Fed program.

Mr. Frost’s task is to avoid paying top dollar for bonds that could be worth less when the Fed tries to sell them one day.

Louis V. Crandall, the chief economist at the research firm Wrightson ICAP, said Wall Street bond traders were driving hard bargains. The Fed has tipped its hand by laying out which Treasuries it intends to buy and when, giving the bond houses an edge.

“A buyer of $100 billion a month is always going to be paying top prices,” Mr. Crandall said of the Fed. “You can’t be a known buyer of $100 billion a month and get a good price.”