For the most part, this is a valid criticism. However, it is not necessarily completely true.
This statement would not be true if the increases in the deficit were caused by what you might call "investments." If the federal government is spending in ways that will make the economy and the nation better off down the road, then this is not a problem. It would be like investing in your grandchildren's future without their consent.
However, if the money is being spent in wasteful ways, ways that do not improve the future chances of the US and its economy, then the criticism is valid. In such a case, the government would be taking out loans that our "grandchildren" would have to pay simply to spend on frivolous things.
So, the accuracy of this statement depends largely on the purpose for which the government is borrowing the money.
Another consideration is whether or not the deficits were "paid off" before one's grandchildren had to pay for them. The previous answer assumes that deficits would never be paid off. If the deficits and the corresponding debt were left for our grandchildren to pay off, then the assumption would become true.