More than 70 percent of respondents to the survey sent to active-duty and reserve military personnel said the effect of repealing the "don't ask, don't tell" policy would be positive, mixed or non-existent, sources told The Washington Post in an article published Thursday.
Based on the responses, the report's authors said objections to openly gay military colleagues would drop once troops began living and serving alongside them.
The report is to be presented to President Obama Dec. 1.
"There are challenges here, and we want the time so we can make the process of implementation as smooth as possible," one person told the Post.
The document is divided into two sections, one exploring whether repealing "don't ask, don't tell" would harm unit readiness or morale, and one offering a plan for ending the ban's enforcement.
The report indicated it didn't think a large "coming out" by gays and lesbians in uniform would happen if the ban is repealed, a person who read the draft told the Post.
Among its recommendations, the report urged ending the military ban on sodomy between consenting adults regardless of what happens to "don't ask, don't tell," the source said.
The report also recommended that gay troops should not be considered a special class for equal opportunity or discrimination purposes, the source said. It recommended few changes to policies on military housing and benefits, because the military must abide by the federal Defense of Marriage Act, which does not recognize same-sex marriage.
The draft also said objections by military personnel who don't want to room or shower with openly gay colleagues should be handled on a case-by-basis.