The balanced budget multiplier implies that when government spending increases (e.g. $1 million) are matched with equal increases in taxes (e.g. $ 1 million), then the net result change to aggregate demand is equal to the government spending increase (in this case it's $1 million). Since the economy is in a recession, an increase of $1 million of government spending (which is a component of AD) would increase AD, moving the economy closer to non-inflationary full-employment. The spending would be financed by the tax increases to alleviate inflationary pressures. So this method would be recommended.