with the Senate
No, the Senate must confirm the President's appointments.
The Legislateive branch must aprove all of Supreme Court appointments
The US Senate (Legislative Branch) has the power to approve or disapprove Supreme Court appointments.
Appointments to the US Supreme Court must be approved by the US Senate.
All Supreme Court appointments must be approved by the U.S. Senate. After the President nominates a candidate for the Supreme Court, the Senate Judiciary Committee conducts hearings to evaluate the nominee's qualifications. Following the hearings, the committee votes to recommend whether the full Senate should confirm the nominee, who then requires a majority vote in the Senate for final approval.
Appointments to the Supreme Court of the US are for life.
president
Congress
Congress must approve all appointments.
The Senate has the sole power to confirm Presidential appointments. The power of "advice and consent" is outlined in the Article II, Section 2, Nomination Clause.
Checks and balances. The Executive branch has power over (checks the power of) the Judiciary branch by way of choosing who to appoint. The Legislative branch has power over (keeps in check) the Judiciary branch by way of choosing whether to confirm the appointments. The Legislative Branch also has power over (keeps in check) the Executive branch because the appointments to the Supreme Court require their approval.
In the United States the Congress, or legislative branch confirms federal judicial appointments. It is the Senate as upper house of the Congress that has the Constitutional power to confirm federal judges, and Supreme Court nominees.