No, the Democrats (or at least Obama) do not want to defund Obamacare, and the Republicans (bar a really clueless one or seven) know that they cannot defund it as long as Obama is in office and wields a veto.
So what was this about?
This was about selectively undoing the sequester cuts. Remember when Congress chose to have the sequestration which enacted roughly half its cuts from the defense department and the other half from everything else?
Well, the CR undoes those defense cuts. Which means that what the House proposed was
- Defunding Obamacare
- Funding defense back to the pre-sequestration levels.
Now the Senate takes this over, and after public posturing sends it back to the House after stripping 1. Boehner can then get this passed and get 2. Saving defense jobs helps politicians of both parties.
That was always the best deal they were going to get, and Boehner will get it. With absolutely no bargaining. If Obama caves in to the debt ceiling hostage crisis (which he has steadfastly refused to negotiate so far) Boehner will get another ounce of flesh.