Zika is just such a threat. It is primarily transmitted by mosquitoes, can cause birth defects and has been linked to neurological disorders in adults. A study published in The New England Journal of Medicine last week estimated that the risk of microcephaly in newborns ranged from 1 percent to 13 percent for women infected with Zika in the first trimester.

A bill introduced by Representative Rosa DeLauro, a Connecticut Democrat, would put $5 billion into an existing public health emergency fund that was created in 1983 but has been largely dormant. The fund currently has a balance of just $57,000. In the Senate, Bill Cassidy, a Louisiana Republican and a doctor, has said he plans to introduce a bill that would provide emergency funds, though he has offered few details.

Some Republicans are likely to oppose setting aside the money. Many in the House have been reluctant to spend money on Zika; last month they passed a bill to provide $622 million to fight the disease, which is a lot less than the $1.1 billion the Senate approved and the $1.9 billion Mr. Obama has asked for.

Despite the concerns of fiscal conservatives, the health emergency fund could save lives and money. Consider Ebola. Had the American government moved quickly to help Guinea, Liberia and Sierra Leone fight that virus early in 2014, the disease might not have killed more than 11,000 people or caused a global panic. But the United States was slow to react, approving $5.4 billion for the disease in December 2014, months after it had caused or was suspected to have caused nearly 7,000 deaths and after Ebola cases had been confirmed in the United States.

That money was used to send doctors and nurses to West Africa, to help strengthen health systems in the affected countries, and for research. Some Ebola projects are still active, including vaccine development and testing. In public health, “the sooner you can get there the more effective you can be,” said Dr. Thomas Frieden, the C.D.C. director. “You can change the trajectory of an epidemic in a way that is very, very important.”