If the economy is in a recession, it is most likely in the Keynesian range of the aggregate supply (AS) curve. This means that the AS curve is flat or nearly so.
If government spending increases and taxes remain steady, there should be (all other things being equal) an increase in aggregate demand (AD). If AD increases, the AD curve moves to the right along a flat (or nearly flat) AS curve. This moves the equilibrium point to the right without making it go up much, if at all. When the equilibrium point moves to the right on an AS-AD graph, real GDP rises. When the equilibrium point goes up, inflation occurs.
If the government increases spending and taxes remain steady during a time of recession, the equilibrium point will move mainly to the right (increasing real GDP) without going up much (thereby not creating much, if any, change in the price level).