TRENTON — Gov. Chris Christie announced on Tuesday a highly unusual special election that was immediately criticized for costing the state $24 million and setting up a schedule that was likely to confuse the voting public. Voters will go to the polls on a Wednesday in October to cast ballots for a new senator, then return just three weeks later for the regularly scheduled general election, in which Mr. Christie will stand for a second term.

For Mr. Christie, a Republican who has cultivated an image as a tough-talking independent, the rapidly made choice represented a calculated risk — to endure short-term criticism from both Republicans and Democrats in order to protect his longer-term goals of winning re-election and positioning himself for a presidential run in 2016.

The announcement was closely watched in Washington, where he will soon send his choice of an interim senator to a tightly divided Senate in which the loss of even one vote complicates efforts by the White House and Congressional Democrats to advance their agenda. Mr. Christie did not announce whom he would appoint to the seat left open by the death of Frank R. Lautenberg on Monday, but said he intended to have someone in the seat by next week, when the Senate takes up new immigration bills.

In New Jersey, the decision to call a special election set off the kind of bitter partisan debate that Mr. Christie has labored to show himself as rising above. Democrats immediately accused him of squandering taxpayer money to protect his own political ambitions at a time when the state budget is under severe stress, and some promised to challenge the decision in court.