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Gov. Chris Christie of New Jersey told his finance team late Friday that he anticipates that Donald J. Trump, who often boasts that he is funding his own campaign, will begin to solicit campaign contributions as the race heads into a general election if Mr. Trump becomes the nominee.

In a conference call hours after Mr. Christie endorsed Mr. Trump, his onetime rival, the governor was asked about what could be done to help Mr. Trump, who says he is a billionaire many times over.

Mr. Christie replied that Mr. Trump, who has won three of the four first nominating contests, is currently self-funding.

But, he added, “I sense that once we get to a general election campaign, that his posture may become different” given the scope and demands of a national campaign, and “how well-funded Hillary Clinton will be on the other side.”

A Times reporter was allowed to listen in on the call by one of the participants.

It was the first time there has been any indication that Mr. Trump might look to raise money in earnest. As of Jan. 31, he had lent his campaign $17 million, federal election reports showed. He has also raised several million dollars, primarily from smaller contributors. Most of his money has gone toward television ads.

But Mr. Trump has said that he is mindful of his costs, and he has repeatedly talked about not wanting to spend money on a pollster or on advertising if he does not have to.

A spokeswoman for Mr. Trump did not respond to an email seeking comment.

Mr. Trump has used “self-funding” as a selling point to voters at his rallies. The claim is only partly true, as money he has raised from donors represents about a third of all the money his campaign has brought in over seven months. The rest is money he lent to his campaign.

That has prompted a number of major donors, who backed other candidates and are now uncertain of what to do, wondering in private conversations about whether Mr. Trump will ultimately seek to secure their support down the road.

But doing so would undercut Mr. Trump’s claim of independence from the party’s major figures, and potentially fuel lingering questions about how much money he has to spend personally.

Yet the Trump campaign is said to be aware of potential pots of money that may be available eventually. According to people briefed on the exchanges, Trump campaign officials have appeared intrigued by how much money would be available to the nominee, and when, through the Republican National Committee should he become the nominee. A spokesman for the party committee did not immediately respond to an email.

Meanwhile, on the finance network call, Mr. Christie also continued his slash-and-burn attacks on Senator Marco Rubio. When a person on the call asked how he would respond to Mr. Rubio’s concerns that Mr. Trump as the nominee would tear apart the Republican Party, Mr. Christie replied, “I would say to Marco that that’s what desperate people say in the last throes of a losing campaign.”

He also pointed out that there was increased turnout in the Republican nominating contests in the first four states, and added that Mr. Rubio had also signed the loyalty pledge that all candidates put their names to last August vowing to support the eventual nominee.

Mr. Christie demurred when asked whether he would appear on a ticket with Mr. Trump, adding, “Donald and I haven’t had any conversations like that at all.”

One donor on the call later was struck by the rawness of Mr. Christie’s anger at Mr. Rubio, whose supportive “super PAC” ran devastating ads that blunted Mr. Christie’s efforts at a political comeback in the New Hampshire primary.