If the government increased its spending on infrastructure when the economy has full employment, its main impact would likely be to draw labor, capital, and raw materials away from various other activities. In effect, increased government spending under these employment conditions would "crowd out" private spending. Measured GDP would not be much affected, if at all. To be sure, the efficiency of the economy would rise if too little had previously been invested in this infrastructure, while efficiency would fall if this government spending were more wasteful than the private spending that was crowded out.
That still won't stop the Democrats from pushing a giant spending bill in the coming weeks. They want to be on record as DOING SOMETHING!