Some Democrats are calling for Obama to immediately appoint Merrick Garland to the Supreme Court. This piece from October indicates he can't.
Clinton Gets the Constitution Wrong on SCOTUS Appointments: A Supreme Court nominee must be confirmed by the Senate in order to be appointed by the president. But for months now the Republican-controlled Senate has refused to consider the nomination of Judge Merrick Garland, President Obama's choice to fill the seat opened by the death of Justice Antonin Scalia. There have been no hearings and no votes—only one-on-one meetings with some senators.
I would hope that the Senate would do its job, said Hillary Clinton during the debate last night, and confirm [Garland]. That's the way the Constitution fundamentally should operate. The president nominates and then the Senate advises and consents or not, but they go forward with the process.
There are some things wrong with this. The Constitution doesn't say what the Senate's job is but leaves that question to the upper chamber. Granted, thanks to the practice in recent decades, we are used to a confirmation process that includes hearings and votes providing consent or denying it. But the Senate is free to do as it thinks best in exercising its consent power.