CHEYENNE, Wyo. (AP) _ Sponsors of the ''National Peace Quilt'' are hoping that each member of the U.S. Senate will sleep under the brightly colored patchwork at some time in 1985.

''The purpose of the National Peace Quilt is quite serious,'' says the newsletter of the peace quilters. ''We want the entire U.S. Senate to understand the depth and breadth of their nation's desire for a peaceful, secure future - and we want them to examine their own personal responsibility for working towars this goal.

''How many senators will be able to refuse? After all, they all have to sleep sometime.''

The National Peace Quilt is the idea of Diane Jones of Boise, Idaho. She has a network of volunteers across the country trying to persuade each senator to sleep under the 10-by-13-foot quilt, which has patches designed by children in each of the 50 states.

''Our little organization here in Boise dreamed it up, but people in every state have helped,'' Mrs. Jones said in a recent telephone interview. ''We're just getting rolling, but I'm really encouraged.''

Some 16 senators have either slept under the quilt or have agreed to, Mrs. Jones said. She expects others to sign up after the quilt hangs in the Capitol during February.

The National Peace Quilt dream started in 1982, when a group of mothers in Boise sewed a friendship quilt and sent it to the Soviet Union as ''a gesture of goodwill,'' she explained.

Since then, they have presented peace quilts to a half-dozen people who have worked for peace, from folksinger Pete Seeger to the late Idaho Sen. Frank Church.

''After sending several quilts abroad, we were talking about how we could make a quilt that would reach our policymakers here in our country,'' Mrs. Jones said. ''We've tried to reach them with the depth of concern that we feel and that we think people all over the country feel.

''Many of us are deeply concerned about the future,'' the 39-year-old mother of three said. ''We need to pay attention to our children and their hopes and fears.''