It is impossible to get it delayed or not funded. For two years Obama has said he will not negotiate on debt ceiling or Obamacare. He has said all those things recently. An article out today also has spoken of his resolve on this. To do any of this it takes his signiture or 21 dem senators to override veto. So even if there is a shutdown how do you win.
I understand your point about polls. Sometimes when you lead you can flip public opinion. The problem is the public has seen 43 times repealing of Obamacare, a court battle, and now a shutdown? They see it as sour grapes. Every poll shows same thing Obamacare is either even or unfavorable by a few points but shutting the gov down over it is toxic.
As a policy move it is a bad play IMO.
The point you might be missing is whose voters benefit the most from the government operating and thus would be hurt the most by it not operating? Do you think if the government does not operate for a bit, the GOP voters will be hurt more or the Dim voters?
So Obama can say whatever he wants. If the GOP Congress will not pass a CR without the Obamacare defunding or delay or if they refuse to raise the debt ceiling without the Obamacare defunding or delay, then the money won’t be there. Obama can huff and puff as much as he wants, but the money wont be there.
Heck a great strategy for the House would be to pass what they will accept and then LEAVE WASHINGTON. They also should refuse to talk to anyone in the national press. Then they can wait until enough Dim voters raise enough sand with Obama and the Dims and then a compromise can be worked out or they can just hold tough until they get what they passed.