Justice Sonia Sotomayor blocked part of the president's signature health care law at the request of Catholic-affiliated groups from around the country just hours before it was set to kick in.
Several organizations, including the Roman Catholic Archbishop of Washington, the Catholic Diocese of Nashville, Catholic University, and the Michigan Catholic Conference, asked the justices to block birth control mandate part of the law until their arguments are heard.
The groups opposed the contraception mandate which forces religious organizations to provide health insurance that includes birth control and drugs that could induce abortions. Religious groups say the mandate violates their beliefs.
Sotomayor said the government has until Friday morning to respond to her order.
In 2012, the Supreme Court upheld the constitutionality of the core of the Affordable Care Act, saying its insurance mandate and the tax penalty enforcing it fell within the power of Congress to impose taxes.
A recent poll showed that public support for Obamacare has hit an all-time low.