In a ground war with conventional weapons, excluding the use of tactical nukes and orbital bombardment. Say a squad of giant fighting robots touches down on the East Coast and is advancing towards New York or DC...
Are they robots or are they Exo-suits? We got little descriptions about the robots so we have to look at some "existing" - Lets go through a few different kinds.
Robots - Autonomous The most famous autonomous robots would be transformers. In the later movies the transformers encounter several different kind of tanks or armored vehicles, but the ability to react move and shoot faster than the tank make them superior. Versus infantry the robots are also superior towards humans. It has been proven that they can be damaged by large amounts of force but it is difficult.
The terminator would be another example, but one would only have to look at the movies to know that it would be vastly superior to normal infantry and tanks. But again not indestructible. A group or individual would be possible but an army would be fatal.
Robots - Dependent An example of a dependent robot would be the robots from the movie Real Steel. This kind of robot would be difficult to go in to direct combat with since it requires wires. Given the possibility to make it wireless. The fearlessness of the robot would make it dangerous. Given the driver uses fear of damage and but not fear of death.
Androids Robocop has the passion and the mind of a human able to make decisions that AI's would have problems with packed in bulletproof armor targeting systems and machine pistol. This make him a dangerous target, but towards tanks and other larger vehicles, we already know that he is vulnerable towards high powered guns.
Exosuits - Giant We got the robots from Pacific rift, able to fight off super monsters, the ability to fight that kind of machine as ground based city fighter would be hard. Though it's vulnerable head makes it possible, but don't count on getting home for dinner.
Exosuits - Large Exo-suits are used a lot in the warhammer 40k universe where both "human" sized suits (Tactical Dreadnought Armor), and larger machines using dead humans to harness it's power exists. Dropping a few Terminators in to a city environment with today's tech would not end well because it combines over-human abilities with mechanical assistance and close to immortality, added with a dash of soldier skills and rocked propelled explosive bullets. It would be pretty ugly.
A more friendly example of exo-suits look at the movie Edge of tomorrow. Here the suit does not provide protection but it provides super human strength and the ability to carry larger guns.
This is really very simple.
If the military can blow up the robots, they win. Think large cannon but especially mines.
If the robots are fast or smart, they win. Assuming reaching NY/DC constitutes a win.
- Robot resupply gives the military an extra round for free as they are fighting on home ground.
- No effect on the "game" if NY/DC are abandoned in a scorched-earth policy and so stop being a target.