WASHINGTON (AP) _ President Reagan says he does not think there is any problem with federal programs to help the hungry and homeless in cities across the nation but he promised to check to ''see if there is some snafu.''

He mentioned at his broadcast news conference Wednesday night that he had just read a newspaper account of a needy family in New York being put up by welfare in a hotel at a cost of $37,000 a year.

''I wonder why somebody doesn't just build them a house for $37,000?'' the president said.

The question about the homeless, the only one on a domestic issue, was asked by reporter Sarah McClendon, who told the president: ''This is a question that won't wait.''

She said that ''it's cold weather out there'' and that the growing number of hungry and homeless have overwhelmed the resources of volunteers.

''They've come back and said we can't feed the hungry and take care of the homeless by ourselves. We've got to have federal help,'' said Miss McClendon, who operates her own news service. ''You have no policy in the White House, I believe to do this, and you are now just leaving this to local government and local groups. They can't take care of it.''

Reagan answered that ''we are still spending more than has ever been spent before trying to help the needy,'' but he promised ''to look into that particular facet.''