Depending on the inverter, some will draw an amp or more at rest with the power on. That's a lot. Also, make sure you use the correct size power and ground cables. These things can require some serious cable.
Also note that some of the cheaper inverters will not effectively work with battery chargers (cell phones, cordless tools, etc) due to the frequency they operate. You'll also see that on some of the cheap ones that the manufacturer does not recommend using them for sensitive electronics, such as laptops. There truly is a difference between a $300 250 watt inverter and a $59 250 watt inverter.