By month’s end, the candidates and their allied groups could spend as much as $100 million combined, much of it on negative advertising delivered via television, radio, mailers and digital spots. And after the effectiveness of positive television commercials came under question last year when tens of millions of dollars failed to lift Mr. Bush, January will offer insights into whether attack ads still have the power they did in past presidential elections.

Mr. Bush’s supporters effectively ended the Christmas truce last week when they went on the air in Iowa with an ad savaging Mr. Rubio over his Senate attendance record and with a New Hampshire commercial contrasting Mr. Bush’s achievements as Florida’s governor with Gov. Chris Christie’s tenure in New Jersey and Gov. John R. Kasich’s record in Ohio. The coming offensive will be just as varied, reflecting the layers of the Republican race.

Mr. Cruz is trying to head off Mr. Rubio, perhaps the only candidate who can build a coalition of conservative and center-right Republicans. Mr. Rubio is determined to slow Mr. Cruz in Iowa, where Mr. Cruz is at or near the top of every poll and could be formidable with a decisive win. But Mr. Rubio also must confront Mr. Christie, who is ascendant in New Hampshire, which votes just over a week after Iowa.

And Mr. Christie and Mr. Bush are both focused primarily on denying Mr. Rubio the sort of strong showing in the two early states that could vault him toward a coveted position in what could be a three-way race: the mainstream Republican best positioned to stop Mr. Cruz or Donald J. Trump from winning the nomination.