Their way.
How bad do they want it?
Bad enough to shut down the government, put hundreds of thousands out of work, destroy the economic security of perhaps hundreds of thousands of families, and cost the economy at least hundreds of millions of dollars.
And they want their way so badly they are willing to take the full faith and credit of this nation and relegate it to the ash heap of history and create world wide economic uncertainty or worse.
Why are they willing to do this? Because they are losing.
When you get into the specifics the conservative agenda has always been unpopular with the majority of people in this country. People want Social Security, Medicare, public infrastructure, and jobs. The people, overall, also support higher taxes on the rich, more regulation on finance, Wall Street criminals going to jail, clean air and water as well as strengthening Social Security and Medicare. Things that are popular with most people are exactly what conservatives are against.
For decades conservatives have had to lie about, or not talk about, their real objectives in the public discourse. Even during the Bush years, when they controlled all branches of the government, many of their objectives were so odious that even that was not enough to get the passed into law. They have had to rely on exploiting a crisis in order to further their goals, and as an extension of that, manufacture their own crises to further their goals.
That is why we are here. The republicans shut down the government to get their way on the Affordable Care Act. The public was against them and President Obama and Democrats held firm. So now they are just running through their shopping list to see what it is they can get for shutting down the government, never mind the cost to the lives of the people they are damaging; republicans don't care.
The Republicans know they must rely on negotiations in a crisis to push through changes that are NOT SUPPORTED by the majority of the people in this country. In terms of gross numbers neither the republicans in the house nor the republicans in the Senate represent a majority of the people in the country. In addition their vote totals were less than those for their Democratic counterparts. They are, in fact, a minority party facing demographic changes destined to push them further into the minority. Their time is now, and they don't care who they hurt.
So what do they want? As much as they can get. They shut down the government to get their way. On something. They're still deciding just what that is. It'll come to them. And in the meantime they will risk the nation's and the world's best credit and do economic and personal damage to hundreds of thousands, if not millions, of lives of people who they do not care about.