NEW YORK (CBSNewYork) — A new CBS News poll indicated that 64 percent of Americans are at least somewhat concerned about a large outbreak of the Zika virus in the U.S. within the next year.

But only 26 percent of respondents are very concerned, and most do not think it is likely that they themselves or a family member will ever get infected with the virus, the poll said.

READ MORE: Nor'easter Topples Trees In New Jersey And New York City, Residents Worried About Others Coming Down

Most respondents also said they would not be comfortable traveling to an area affected by Zika, whether inside or outside the United States.

MORE ON ZIKA FROM THE CDC: Basics | FAQ | Info For Pregnant Women | Symptoms, Diagnosis & Treatment | 10 Facts About Zika

The greatest risk posed by Zika is to unborn babies, who can contract severe fetal brain defects if their mother is infected. Concern about the virus is much higher among Americans who have a family member who is or is trying to become pregnant – with 40 percent among that group very concerned.

A total of 64 percent of respondents also believe the federal government is not prepared for a large Zika outbreak, and 57 percent want Congress to approve more funding for Zika, the poll said.

READ MORE: Candidate Conversations: Curtis Sliwa

A minority of Republicans favor more funding – topping out at 39 percent. Most Republican respondents said enough is being spent already.

But 70 percent of Democrats and 57 percent of independents favor more federal funding for Zika.

On Tuesday, Mayor Bill de Blasio and U.S. Rep. Carolyn Maloney (D-N.Y.) called on Congress to pass emergency funding to help fight Zika.

De Blasio said Tuesday that there are 480 confirmed cases of Zika in New York City. Most appeared to be connected to travel to affected areas.

The city has tested more than 3,400 pregnant women for the virus, and 49 tested positive. One baby was born with microcephaly due to Zika, de Blasio said.

MORE NEWS: Bullet Believed To Have Been Fired By Alec Baldwin Recovered From Film Director's Shoulder

A U.S. travel warning was recently issued for a neighborhood in Miami where Zika is being spread locally by mosquitoes.