And if the Senate had been operating under majority rule during the Obama and Bush administrations, the following bills would have gained Senate approval: the Toomey-Manchin background check bill for guns; the provision allowing people to have a “public option” for health care on the Obamacare exchanges; comprehensive immigration reform; an increase in the minimum wage; and the bipartisan campaign finance bill, called the Disclose Act.
The lack of a filibuster for legislation will require members of congress to put up or shut up, they won't be able to hide behind the obstruction of the minority party. I'm fairly certain it will be abolished before the midterms, the Democrats will most likely filibuster most (all?) of the Republican agenda to keep their base happy and punish McConnell. McConnell will respond with another nuke.
The only concern I have left is the effect the lack of a filibuster (both legislative and non-legislative) will have on the Supreme Court. The size of the Court is defined by statute, not constitutional law. It seems to me that one wrong ruling will lead to another court packing scheme (let's call this the Tsar Bomba option) and without a filibuster, the majority party will have no problems getting it passed. Given the stakes, I find it hard to believe that either party's base would be opposed if their guys were in power.
On the other hand, there are supreme courts in the world larger than ours. The Supreme Court of Sweden has 16 members, Israel has 15, and Norway has a staggering 20. A larger court would probably lead to less dramatic confirmation hearings since the impact that any one justice has would be lessened. Not to mention that there would be a more regular supply of dying/retiring justices in need of replacing.