log-roll (v.)

also logrolling, in the legislative vote-trading sense, "mutual aid given in carrying out several schemes or gaining individual ends," 1823, American English, from the notion of neighbors on the frontier joining forces for rolling logs into heaps after the trees have been felled to clear the land (as in phrase you roll my log and I'll roll yours); see log (n.1) + verbal noun from roll (v.). "Sometimes many neighbors were invited to assist, and a merrymaking followed. [Century Dictionary]. In lumbering, in reference to rolling logs into a stream where they bound together and floated down to the mills.

LOG-ROLLING. 1. In the lumber regions of Maine it is customary for men of different logging camps to appoint days for helping each other in rolling the logs to the river, after they are felled and trimmed — this rolling being about the hardest work incident to the business. Thus the men of three or four camps will unite, say on Monday, to roll for camp No. 1, — on Tuesday for camp No. 2, — on Wednesday for camp No. 3, — and so on, through the whole number of camps within convenient distance of each other. [Bartlett]

However the phrase is not attested in any literal sense, only the political sense, until 1848.