No, that's not how the process typically works.
Typically, the Administration provides some leadership, giving guidance as to where the goal line is, so the Congress isn't off negotiating futile efforts.
The key word there, Suppressed, is "typically". Trump's not providing leadership. Earlier this week he said he'd sign whatever bill Congress puts before him. Later he rejected the "Gang of Six" proposal, but didn't further advance the ball. (Of course, that's in large part because of Dicky Durbin poisoning the well for bad-faith political reasons, by revealing Trump's alleged "shithole countries" remark made during a private discussion.)
The Dems don't want a bill, and Trump won't say what sort of bill he'd sign. That's a recipe for a collision. I guess each side thinks it will win the battle for public opinion when the government shuts down. The Dreamers? Who the flip cares about them?
And that's NOT how the process is supposed to work.