Quite probably. However, if they rule that it is severable, their heads may be heard exploding all the way to California.
In this article, published last October, I suggested that
For the Supreme Court to agree with the Eleventh Circuit that the mandate is unconstitutional and to allow the rest of the law to remain standing would be the worst possible outcome for President Obama. That is what all judges who have found the individual mandate unconstitutional have done, with one exception.With that result, ObamaCare would resemble an ObamaCare patient, sick and dying but unable to get nourishment. The Dems have no viable solution to offer, because there is none. That result would revive ObamaCare as a campaign issue to a far greater extent than would a Supreme Court decision killing it outright.
Although for other reasons I would prefer to see ObamaCare killed outright, for defeating President Obama the mandate amputation procedure would be superior.
If the mandate fails, but all else remains in place, we will end up with socialized care anyway. Because there will no longer be any private insurance left.