Why does the government have to take the multiplier effect into account?

The multiplier effect occurs within the circular flow of money, more precisely when people earn income and spend a proportion of what they have earned. When the government invests in infrastructure (for example roads) then construction workers earn money. They in turn spend it on goods and services they may not have bought, if they had less money to spend/were unemployed. Through this spending everyone from bakers to car manufacturers or restaurants may earn more (or at least the businesses where those people work in do). Hence the money the government inject into the economy may multiply and the results seen in the economy (measured by GDP for example) may be far greater than the investment from the government.
The government will need to take this into account, because it could reduce their spending and thus interests and debt the government has to pay back. (Also crowding out may be reduced, but that is another topic)