Yes, some financial institutions are systematically important to the economy in the sense that the failure of one of them could trigger global financial crisis. These companies are tightly woven with the United States economy, and employ so many people that were they to vanish, a global finanical crisis would be likely.
The concept of the failure of a financial institutions having the capacity to trigger a global crisis is sometimes difficult to wrap your head around. Instead, if one looks at the issue in a hypothetical smaller scale one can see the possible repercussions. Imagine a small community with two major industries as the primary employers. If one of the companies were to suffer a failure, it would effect the entire community. Jobs would be lost, which in turn would effect the local economy. People would be unable to pay for basic needs such as housing and utilities. Mortgages would be defaulted on and those who rent would no longer be able to afford their housing costs as well. Money which had gone into the local economy through the sale of goods to the displaced workers would also be lost. If jobs were not available, many of the workers would leave the community. To make up for the lost income, the local government would be forced to raise taxes, which may put the remaining industry in jeopardy. However, if the community were able to offer tax breaks, incentives, and possibly loans to the failing industry, it could be saved and thereby save the community as a whole.
There are some financial institutions which because of their size and the vastness of their investments could have the same effect on the global community. If they fail, we all suffer the consequences.