Katie Packer, a Republican strategist overseeing Our Principles, said the group’s ads had helped reduce Mr. Trump’s margin of victory in South Carolina. “Our hope is that the field will winnow and conservatives will coalesce behind a candidate that believes in conservative principles and can unite the party,” Ms. Packer said. “We intend to keep the heat on in Nevada and the March 1 states and as long as it takes for that to occur.”

Mr. Kasich had just $1.4 million on hand at the end of January — virtually dry against the scale of modern presidential campaigns — while Mr. Rubio had $5 million, though both campaigns were expected to capitalize on strong showings in the first two contests. After spending tens of millions of dollars between them, the “super PAC” backing Mr. Kasich reported only $2.4 million in cash on hand, while the group backing Mr. Rubio had $5.6 million.

The disparity between traditional and insurgent candidates was echoed to some extent on the Democratic side, where Senator Bernie Sanders of Vermont raised almost $6.5 million more than Hillary Clinton in January — the first reporting period in which his campaign has taken in more money. Virtually all of that money came from donors giving small checks.

But Mr. Sanders also spent heavily to win in New Hampshire and fight Mrs. Clinton to a virtual tie in Iowa, dropping $35 million in January, reports filed late on Saturday showed. He ended the month with less than half as much cash on hand as Mrs. Clinton.

A super PAC backing Mrs. Clinton, Priorities USA Action, also continues to stockpile cash, reporting $45 million in cash on hand at the end of last month. The group took in almost $10 million in January, including $3.5 million from James H. Simons, a retired hedge fund founder from New York.