In this paper, we analyze the equilibrium of a sequential game-theoretical model of lobbying, due to Groseclose and Snyder (Am Polit Sci Rev 90:303–315, 1996), describing a legislature that vote over two alternatives, where two opposing lobbies compete by bidding for legislators’ votes. In this model, the lobbyist moving first suffers from a second mover advantage and will make an offer to a panel of legislators only if it deters any credible counter-reaction from his opponent, i.e., if he anticipates to win the battle. This paper departs from the existing literature in assuming that legislators care about the consequence of their votes rather than their votes per se. Our main focus is on the calculation of the smallest budget that the lobby moving first needs to win the game and on the distribution of this budget across the legislators. We study the impact of the key parameters of the game on these two variables and show the connection of this problem with the combinatorics of sets and notions from cooperative game theory.