If we look back on President Obama's record, he has a history of making centrist decisions when it comes to issues where there is a lot of partisan rancor. The Affordable Care Act, doesn't have a single payer system, because President Obama caved to Republican pressure and didn't press the issue. Most of his first two years in office were dedicated to trying to appease Republicans and gain their support. So now that we are in a situation where a Supreme Court vacancy exists, Republicans have only three realistic options.
They can wait until Nov 2016, in which case Hillary Win's and nominates someone slightly left of center. Given her background working for Goldwater, her history of supporting and being funded by corporate special interests, and her pandering nature to act like a political weather vane, I don't expect her to nominate someone who is strongly liberal, but if she wants to be a Two term president, she would need to nominate left of center, even if it was only slightly left.
The second option is to wait until Nov 2016, in which case Bernie Win's and nominates an outright liberal to the court, decisively tipping the ideological scales firmly 5 - 4 in the Democrats favor. I think this is a pretty safe assumption, given his Democratic Socialist ideological beliefs and his record over the last 40 years.
That leaves us with the final, and perhaps best option Republicans can hope for, letting President Obama nominate a centrist to the court. I saw centrist, because President Obama has not been a liberal president, despite what right wing and conservative media say. He has consistently been a centrist politician, sometimes voicing more liberal social values, but acting from a centrist position. I see an Obama nominee as being someone who will be as close to neutral as is possible without veering to the right. I don't think he would try to nominate someone who is any further left, due to the highly partisan atmosphere in Washington, and someone who is centrist, with a recent confirmation under their belt already, would stand a better chance of peeling away Republican support from their staunchly obstructionist caucus.
So, if Republicans want to have a court that is not a reliable 5 - 4 split in the Democrats favor, their best bet would be to let Obama nominate someone, and confirm that person before the 2016 election. Now I say these are the three options they have, because it is not only possible, but probable that Republicans will not control the White House again for a very long time, especially after the hard right swing they have done over the last 8 years. The country is moving further toward the left, while Republicans have moved harder to the right. This may win them base support but it loses them the majority of the electorate who have moved on without them.