The votes of Maine’s Sens. Olympia Snowe and Susan Collins can be decisive in the current flurry of issues on which the Bush administration is desperately seeking victory: the John Bolton nomination for United Nations ambassador, controversial judicial nominations, an administration attack on the filibuster rule and partial privatization of Social Security.

We may not know for a long time what sort of behind-the-scenes horse trading may be taking place this time, but a look at history can be instructive. Forty years ago, President Lyndon B. Johnson, an expert on what buttons to push to whip reluctant members of Congress into line, needed a few more votes to break a long Southern filibuster and win enactment of the historic Civil Rights Act of 1964. Cloture in those days required a two-thirds vote. His target was Carl Hayden, an Arizona Democrat. Mr. Johnson saw that a Hayden switch could bring along several other Southerners and win the battle.

A new book about President Johnson, “Judgment Days” by Nick Kotz (Houghton Mifflin), tells how he did it. Mr. Kotz writes: “After the president’s weekly breakfast with Democratic congressional leaders on May 5, he asked Hayden to stay behind. If Hayden would consider voting for cloture, Johnson told him, he would consider approving the long-delayed Central Arizona Project, a multibillion-dollar plan to bring water to Phoenix and Tucson from California, a project Hayden had been pushing for sixteen years.” Mr. Hayden agreed to the secret deal, and his switch brought along enough other senators to break the filibuster.

Like President Johnson, Mr. Bush also knows what buttons to push. The House vote on Medicare, for instance, was delayed while his supporters finally got enough votes for a knife-edge victory. Now he needs the votes of Maine’s moderate Republican senators in his efforts to win the Bolton confirmation, the Social Security changes, the judicial confirmations and partial abolition of the filibuster.

The Pentagon’s recommendation that the Portsmouth Naval Shipyard be closed and the Brunswick Naval Air Station be cut back offers Mr. Bush a bargaining opportunity reminiscent of the Lyndon Johnson era. Though the closure decision is supposed to be apolitical, nothing in Washington is apolitical.

Maine’s two senators are so independent on such issues that they could turn White House pressure into a political asset in a state where the majority did not vote for George Bush. The challenge for all presidents is in knowing which issue to press on and when to back off. Lyndon Johnson, as “Judgment Days” shows, was a master.