I can see why this process and posturing could be disturbing to some, but I am not too bothered by it. That's politics, and like it or not, politics has deeply infiltrated every aspect of our system, even our Constitution, and the legal system. If it weren't for politics, every Supreme Court decision ought to come back 9-0, based purely on reasoning and logical consistency with the Constitution and other legal rulings. Yet we have the opposite. Supreme Court decisions often come down split 5-4 over party lines, or other ideological or political alliances amongst the justices on specific types of issues. And there are those Supreme Court decisions that seemingly overreach the purview of the Constitution, and seem purely motivated by the justices' personal ideals and prejudices, such as the gay marriage ruling.
Regarding Obama's constitutional responsibility to nominate a replacement for Scalia, I am guessing there is some wiggle room or gray area in that. After all, if Scalia had instead died one day before the end of Obama's term, would Obama still be forced to nominate a candidate? While he may have the responsibility, I am guessing he is not obligated by duty to do so within a certain time frame, in which case it is completely reasonable for the Republican party to vocally oppose an Obama nominated successor.