There may be some confusion over the terms Budget Reconciliation and Nuclear Option. They are not the same. I'll try to describe how they are different.
Budget Reconciliation
The legislative process known as Budget Reconciliation goes back to 1974. It is an optional process that Congress sometimes uses with legislation that includes policy changes with regard to the federal budget; specifically, funding of mandatory programs and/or revenue programs (anything dealing with taxes).
Many bills dealing with federal budget items are voted on without the use of the Budget Reconciliation process, but it has been used from time to time. From 1980 to 1998, Budget Reconciliation was used 13 times. More recently, this process was used four times during the Bush administration, including both the 2001 and 2003 Bush tax cuts.
It is important to note that Budget Reconciliation is an established legislative process that Democrats and Republicans both have used in the past, and will no doubt use again in the future. A very good description can be found here:
THE BUDGET RECONCILIATION PROCESS (http://www.rules.house.gov/archives/bud_rec_proc.htm - broken link)
Nuclear Option
This phrase describes something that does not exist. The phrase is generally attributed to Republican Senator Trent Lott, and it refers to an effort by Republicans to change Senate rules regarding judicial nominations.
In a nutshell, it takes a two-thirds vote in the Senate (60 votes) to break a filibuster. In 2004/2005, although the 55 Democrats in the Senate had agreed to over 200 Bush judicial nominations, they used the filibuster process to block 10 appointments to the bench, and that caused Republicans to seek a way to change the rules.
There are very good articles giving the background of this available here:
The Political Scene: Blowing Up The Senate : The New Yorker
Everything you wanted to know about the "nuclear option" - Salon.com
The Nuclear Option was never approved, and therefore has never been used. The so-called
Gang of 14 worked out a compromise.
So, with any current legislation, it's Budget Reconciliation, and not Nuclear Option.