WASHINGTON—After decades spent seeking universal health care, Democrats are considering moving legislation that would set that goal aside, yet again.

The debate is highlighting a contradiction present from the start of President Barack Obama's effort to overhaul the health-care system: Advocates have long been uncomfortable selling the bill's central feature, a significant expansion of health-care coverage, and instead chose to highlight cost cutting and insurance reforms.

The late Sen. Edward Kennedy called universal coverage "the cause of my life," and bills passed by both chambers of Congress would expand insurance coverage to 30 million or more Americans. But the Obama administration rarely sold its plan as a way to cover the uninsured, believing that message wouldn't resonate with most Americans, who already have health insurance.

Democratic Party leaders are giving rank-and-file members of Congress the weekend to think through their options, hoping they will decide they would rather have an ambitious bill, which would cover about 95% of people in the U.S., despite the political risks of supporting something that has proven unpopular.

Options include modest coverage for the uninsured, perhaps aid for small businesses, new rules for insurance companies and some policy changes to control federal health spending. Decisions are likely to wait until after Wednesday's State of the Union speech.