WASHINGTON — As a congressman from Buffalo, Brian Higgins is usually on the receiving end of entreaties from high-powered lobbyists. But with state lawmakers in Albany and nationwide preparing to redraw their electoral districts, Mr. Higgins has turned the tables, appointing his own lobbyist to try to save his district — and his job.

Mr. Higgins, a Democrat, hired a longtime Albany insider, the former majority leader of the New York Assembly, Paul Tokasz, to do his bidding in the once-a-decade process of recarving the state voting map. With so much riding on the outcome, “you can’t leave it to chance — you have to be aggressive about it,” Mr. Tokasz said.

Now that census population figures have been tallied and redistricting is beginning in earnest, hundreds of officials around the country are relying on a wide array of political tools — some unorthodox, many old standbys — to try to keep their grip on power, or pry it away from their opponents.

Beyond hiring lobbyists, major players in Washington — including high-priced lawyers, union officials, House leaders and national party operatives — are spending time and money to influence how officials in state capitals design the political maps that will affect the balance of power in Congress for the next decade.