I believe that was the original purpose yes but that it can be applied to any budget bill. Here is an overview you can refer to. But the gist of it is that once the House has passed a budget bill the Senate can bring that exact same bill to the Floor even if they don’t have the support of 3/5 of the senators. And if the party that controls the Senate doesn’t also control the House then the legislative filibuster isn’t as important to begin with.
Now is an excellent time to further weaken or even remove the filibuster from the Senate. The Democrats have lost control, but still have the rest of the year with a lame duck majority. They can enact filibuster reform and it will be clear that they are doing it not for immediate political advantage but because it will improve the function of the Senate.
There will be some short-term pain, since the Republicans next year will be able to send bills to the White House more easily. But with a Democrat waiting there wielding a veto pen, and with no threat of overridden vetoes, the damage will be minimal. Actually, I think removing filibusters would hurt the Republicans–I don’t think they have the self-control to not pass craziness that Obama can easily veto for political advantage.
The filibuster is an archaic practice that gives too much leverage to the minority party (exacerbated by the per-state rather than per-capita representation). I don’t expect Republicans to do what’s best for the institution, so that leaves the Democrats. A lame-duck majority is the best shot to get the filibuster improved or removed.