What did you guys think "be a check on a Clinton Presidency" means? This is a winning message for Senate Republicans.
This goes beyond being a "check". The Senate is supposed to confirm the president's nominee unless there's actually a good reason not to. It's shameful to block nominees simply for partisan reasons.
No, the Senate has an equal say as the president. Both sides have to agree, or the candidate will not be confirmed. Nowhere does it say that the Senate has to find a non-ideological reason to reject a nominee.
But it has been a tradition to allow the president to appoint someone from their own party. That doesn't mean you should approve a Goodwin Liu, but if Clinton puts up Sirvansian or renominates Garland, you guys need to approve it. As much as you and McCain may disagree, your party's official position is "let the next president decide".