The president has the congressional power to nominate a new justice. That said, the Congress has the responsibility to review the nominee. Then, Congress can decide, in a vote, whether or not the nominee is appointed. Although, congress does not have to agree to a nominee of even review one.
Last I checked, we are paying the salary of congress and the President to undertake the legislation and governance of the country. The current position of republican members of congress is tantamount to theft; they continue to collect a tax-payer funded salary and do absolutely nothing to benefit their constituents or participate in the process. The constitution is pretty clear on this one.
As per the democratic process in the United States, the Chief Justice of Supreme Court is appointed by the President of the United States. Even though Obama's tenure is ending , he should appoint the Chief Justice as it will ensure with holding democratic conventions set forth by the founding fathers of US constitution.
President Obama should appoint the next Supreme Court Justice because there is almost a year left in his term, which is enough time for it to be reasonable for him to appoint the justice. It is the duty of the President to appoint judges to the court and just because it is an election year does not mean he should not fulfill his presidential duty.
The United States Constitution clearly gives the president the right to make judicial appointments with the consent of the Senate. Obama is the current president, and so it follows that he has the constitutional right to make this appointment. The Senate can of course reject his nominee, but they have a responsibility not to if the appointment is reasonable and well qualified. It is important to honor the Constituion and the balance between different branches of goverment.