US Senate Republicans have doubts that they will be able to repeal Obamacare and pass new healthcare legislation.
The delay is a huge blow to Trump and Republicans who have spent the last seven years plotting an end to the Affordable Care Act, commonly known as Obamacare.
The 142-page draft repeals most of Obama's health care reforms. The Senate plan phases out the expansion of Medicaid and repeals taxes on the wealthy and insurance companies.
A healthcare bill being unveiled by US Senate Republicans this week is expected to roll back the Obamacare expansion of the Medicaid healthcare programme for the poor and reshape subsidies to low-income people buying private insurance.
The US House of Representatives on Thursday narrowly approved a bill to repeal and replace Obamacare, handing President Donald Trump a partial victory as the healthcare legislation now heads to the Senate.
Residents of Beattyville, Kentucky voted for Donald Trump to become US president because of promises he made to bring back jobs. Another campaign promise - repealing Obamacare - could add to their pain.
The White House played down suggestions that the vote was delayed due to lack of support saying it would take place on Friday and would pass.
Opposition Democrats have warned against repealing the former president's healthcare plan, saying it will leave tens of millions of Americans without access to affordable medical care.
At least 24 million Americans are expected to lose their health insurance if Obamacare is replaced with the Republican-backed American Health Care Act. The poor, the sick and the elderly are expected to suffer the most.
Trump administration yet to endorse the Republican legislation. Former US president Barack Obama's Affordable Care Act enables about 20 million previously uninsured people to get medical coverage.
Vice President Mike Pence, White House chief strategist Steve Bannon and Chief of Staff Reince Priebus called for Republican unity ahead of the US president's appearance at the conservative conference.
One of the biggest objectives of the new Republican administration is to repeal the outgoing president's signature healthcare programme.
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