The President should set a number such as 35%, and allow as much as possible the Republicans to control that much in the Stimulus bill and others that follow.
In return they have to guarantee a certain number of votes.
On the current bill, I suggest 15 senators, and 70 House members.
So if the Obama team puts forth a $1.2 trillion stimulus package, there should be around $400 billion or so that is completely controlled by the Republicans. This can be marginal tax rate cuts, infrastructure spending, or some other stimulus they believe in.
They can negotiate up or down from the percentages, but Obama should force them to agree to the deal before the details are hammered out.
If they refuse, let the public know that Democrats offered up a healthy dose of bipartisanship and now it is time to govern.
I think it is important we define things rather than let it be subject to political speculation.