Republicans decry the strategy of acting on such issues during the lame-duck session, accusing Democrats of playing politics and ignoring the message voters sent Nov. 2. [See photos from the campaign trail.]
But Democrats also face pressure from their left flank.
Gay-rights groups have criticized Reid for not pushing hard enough to repeal the "don't ask, don't tell" policy against openly gay soldiers, as the House has already voted to do.
Reid has promised to hold a Senate vote on the matter before year's end, after hearings can be held later this week on a Pentagon report on the impact that openly serving gays would have on the military.
Republicans say they need to examine the report, which was issued Tuesday, before acting. It concluded that getting rid of the policy might cause some disruption at first but wouldn't create widespread or long-lasting problems.
Obama seized on the conclusion to call on the Senate to act "as soon as possible" to repeal the ban, "so I can sign this repeal into law this year and ensure that Americans who are willing to risk their lives for their country are treated fairly and equally."