The outside activity is not confined to Republicans. Mr. Obama’s campaign apparatus has transformed itself into a nonprofit political group, though it said it would disclose the names of its donors (and it is not getting involved in the Hagel fight).

After Mr. Obama won re-election in November and Democrats kept their majority in the Senate and made inroads in the House, Republican Party officials and senior strategists with conservative outside groups predicted that some of the big financiers of the larger outside efforts would pull back and reassess their involvement and whether their millions were wasted. But while the donors have said they will insist that the groups they finance find lessons in last year’s losses, their interest and stakes in what happens in Washington have certainly not waned.

For instance, the biggest individual financier of the so-called super PACs that sought to defeat Mr. Obama, Sheldon Adelson, is so invested in the fight over Mr. Hagel that he has reached out directly to Republican Senators to urge them to hold the line against his confirmation, which would be almost impossible to stop against six Republican “yes” votes and a unified Democratic caucus.

Given the more than $100 million he donated to the anti-Obama effort last year, no lawmakers need to be reminded of his importance to their future endeavors. People briefed on his involvement said Mr. Adelson, chairman of the Las Vegas Sands Corporation and a longtime supporter of Israel, was calling in conjunction with the Republican Jewish Coalition, a group he has financed for several years.

In an interview with The Wall Street Journal in December, Mr. Adelson said he was prepared to “double” his investment in politics in the coming year.

But it is unclear whether he is directly financing any of the anti-Hagel advertising. An associate of his, speaking about Mr. Adelson’s thinking on condition of anonymity, said he did not believe that expensive television campaigns are the answer to every political push given that Mr. Obama’s re-election team accomplished so much of its success through online and volunteer efforts.

Image The last major cabinet skirmish, over President George W. Bush's nomination of John R. Bolton as the United States ambassador to the United Nations, had no comparable outside media campaign.

Citing similar reasons, another major Republican donor, Foster Friess, said in an interview that he had developed his own skepticism over “the whole idea of these multimedia ads from 45,000 feet.” After last year’s losses he said he was devoting most of his resources to an effort he called “Left-Right, Left-Right Forward March,” which finds projects liberals and conservatives can support together, like water purification in developing countries.