The above crass idea is promoted by many in high places: for example The Economist, the U.S. Treasury, Brad DeLong and Larry Summers.
The first and obvious flaw in the above argument is that infrastructure investments last for DECADES. And there is no reason to suppose that current low interest rates will last that long. Doh!
Second, a monetarily sovereign government does not need to borrow, since it has the power to print. So never mind interest rates being LOW: such a government can obtain money at NO COST AT ALL!!!!!
So would it make sense for government in a recession to fund infrastructure investments with freshly printed money? The answer is “no”: because in order to best allocate resources as between investment goods and consumer goods, some sort of FREE MARKET rate of interest should be debited to the relevant investment – not the artificially low rates at which government can come by money.
In fact it has long been recognised by the economically literate that even when a country is NOT IN A RECESSION, government should not calculate the merits on investment projects on the basis of what it costs government to borrow. Reason is that government has an unfair advantage when it comes to borrowing: it is an ultra credit worthy borrower on account of its ability to extract money by FORCE from the population.
I dare say the Italian Mafia can borrow at relatively low interest rates and for similar reasons. That does not mean that investments made by the Italian Mafia are particularly clever or worthwhile.
In a recession, the conventional wisdom is that governments should cut interest rates. Why on Earth investment goods should suddenly become more worthwhile relative to consumer goods just because there is a recession is a mystery. In fact the whole idea is a load of codswallop. That is, there is no good reason to boost investment spending rather than consumption spending in a recession.