The chips are rated for 2A if they are on a perfect heat sink and a very heavy multi layer pc board. Some of the chip's heat goes into the heat sink. Most of it *should* go into the pc board through thermal via's under the chip. You can move a *lot* of heat with a multi layer board and good via patterns. The little modules you get with the chips on them are far from ideal pc boards and the heat sinks are very small.
The heat in the chip goes up as the square of the current. It's going to need 4X the cooling at 2A as it does at 1A. The chip will shut down to protect it's self, but it does this well above the temperature you should be operating it at. They set the cutout point to take care of catastrophic failures. It's not there for normal operation. People have reported cut out issues with these drivers in the 1.2 to 1.5A range. That would suggest in their case that operation above about 1A probably isn't a good idea.
Nothing says you have to run the motors at their max current (or that it's a good idea to do so). The real question is whether you will get enough torque running those motors at half current.
