The justices were scheduled on Friday to consider the state of Virginia's appeal seeking to invoke a rarely used procedure to bypass the normal appeals process and speed up a Supreme Court ruling on the law's constitutionality.
Legal and financial analysts expected the justices to reject the request.
In orders released on Monday, the Supreme Court took no action in the case. The court did not grant Virginia's request, nor did it deny it, as the Obama administration has urged.
The justices often take no action in a high-profile case when they want more time to consider it. The justices could consider the healthcare law again at a private conference on April 23.
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Several federal trial judges around the nation have upheld the law but others declared it unconstitutional on the grounds Congress overstepped its authority in requiring that Americans start buying health insurance in 2014 or pay a penalty.