US Republicans eager to repeal "Obamacare" suffered a deeply embarrassing setback on Tuesday when shrinking support forced them to postpone votes on their controversial health care overhaul, one of President Donald Trump's top priorities.

With the Senate bill delayed by a few weeks and maybe more, the timeline of the effort - and the overall viability of a years-long bid to dismantle Barack Obama's Affordable Care Act in favour of a Republican replacement - was thrown into question.

Senate Majority Leader Mitch McConnell acknowledged he simply did not have the votes, after a grim, non-partisan forecast projected the bill would leave 22 million fewer people insured by 2026, as compared to current law.

McConnell said party members would "continue the discussions within our conference on the differences" that they have.