The Republicans have gone a long way towards highlighting what's wrong with democracy. How can a section of the government bring the entire government to a standstill because they don't agree with the President? The President was elected by the American people and just because he doesn't belong to the right party doesn't give elected officials the right to act like toddlers.
At this point it is all about principles. The senate wants to tarnish his legacy by any means necessary (how ironic is that, as this sentiment is a Malcom X mantra). They are thinking only about the next election and looking strong to their constituents. They want to be the senator who stood up to the president. It truly is only smoke and mirrors though.
Yes, Senate Republicans have no incentive to stop fighting President Obama. They are currently refusing to hold committee hearings for the President's Supreme Court Nominee, Merrick Garland. Republicans have more to gain from blocking the President's agenda as it is an election year. Their base hates Obama, and they score cheap political points by grandstanding and blocking his agenda.
The Senate is controlled by Republicans, while our President is a Democrat. These two camps have been at odds throughout the duration of Obama's presidency. This antagonism shows no sign of stopping, even as Obama's term comes to a close. Senate Republicans are simply unwilling to compromise with him on any issue.