Not something I’ve studied in any depth, but there is this paper by Randolph Sloof:
We characterize equilibrium behavior in a finite horizon multiple-pie alternating
offer bargaining game in which both agents have outside options and threat points. In contrast to the infinite horizon case the strength of the threat to delay agreement is non-stationary and decreases over time. Typically the delay threat determines proposals in early periods, while the threat to opt out characterizes those in later ones. Owing to this nonstationarity both threats may appear in the equilibrium shares agreed upon. When the threat to opt out is empty for both agents, the outcome corresponds exactly with the (generalized) Nash bargaining solution. The latter observation may prove useful for designing experiments that are meant to test economic models that include a bargaining stage.
In other words, I am not surprised they are on the verge of reaching a deal. The features determining behavior in the earlier periods are not the same as the features determining behavior toward the end. Low “delay costs” do not mean low “no deal at all” costs, especially for the Republicans.