Selecting a Nominee
For the Supreme Court
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Consideration over this factor is simply not just looking beyond the ranks of the federal judges but also is impacted by candidates who are both qualified and are willing to accept the nomination.
The president will want to appoint someone who agrees with his or her views. This is impacted by the chance of not always having the "perfect" candidate who agrees in all the views with the president, so issues will always have a possibility of generating under certain topics.
Majority in the Senate
If the Senate is ruled by the opposing party, the president will have a difficult time getting a confirmation on a nominee with radical views. If the president's party controls the Senate, it will be much easier to confirm a nominee with views in line with that party, but it could still have a political cost in terms of public approval.