“$5 billion in additional off-budget Overseas Contingency Operations funding is not an acceptable substitute for determined leadership to confront the growing threat of global terrorism,” Sen. Mark Kirk told The Daily Beast. “The administration has already asked for nearly $8 billion in International Security Assistance funding, which includes both international military training and financing programs. I am curious to learn more how this new ‘fund’ would make Americans safer and enhance the United States’ leadership abroad.”

In his speech, Obama noted that “a critical focus” of this new fund would be “the ongoing crisis in Syria.”

A senior administration official told reporters Wednesday that any effort to train the armed Syrian rebels would have to come from the new fund, if it materializes. The official said the fund was “to deal with different contingencies across the region,” and was affordable because of the president’s decision to draw down the U.S. troop presence in Afghanistan.