The Obama campaign on Tuesday shrugged off reports showing that Republican challenger Mitt Romney outpaced the president by $35 million in contributions last month, even after firing off a dire message to donors warning of defeat in November if fundraising doesn’t improve.

“We are sticking to the fundraising course we set from the beginning,” Obama campaign spokeswoman Katie Hogan said. That means, she said, that the team will continue to grow a base of donors — which it currently places at 2.4 million — who are able to contribute small amounts throughout the campaign.

“We’ll stick to the course we know, which is that the more people you get involved in any way possible is how you win,” she said.

June fundraising totals released Monday show that Romney raised $106 million in conjunction with the Republican National Committee, while Obama and the Democratic National Committee brought in $71 million. The $35 million difference is more than twice the financial edge Romney held in May.

The widening gap added to Democrats’ sense of urgency, given the unprecedented cascade of cash flowing from conservative groups that have no legal limits on fundraising. In an e-mail sent to donors on Monday, Obama campaign chief operating officer Ann Marie Habershaw said it is critical that the president at least stay close to Romney in the money race. “We will lose if this continues,” she wrote.

Another Obama campaign official, who spoke on the condition of anonymity to be candid, said Tuesday that although no major shake-up in the fundraising operation is being contemplated, the campaign remains deeply concerned about the super PACs aligned with Romney and will intensify its efforts on multiple fronts. In addition to pursuing serial donations from small-dollar contributors, it will double down on major donors who have yet to reach their legal maximum. The campaign also will aggressively pursue 2008 donors who have not given in 2012, the official said.

Obama representatives also blasted the Republican super PACs. “You’ve got a few very wealthy people running around trying to purchase the White House for Mr. Romney,” White House senior adviser David Plouffe told ABC’s “Good Morning America” on Tuesday.

The campaign followed up with an e-mail appeal to donors signed “Barack.” It said in part: “We’re getting outraised — a first for a sitting president, if this continues. Not just by the super PACs and outside groups that are pouring hundreds of millions of dollars into misleading ads, but by our opponent and the Republican Party, which just outraised us for the second month in a row.”

The Obama camp appears to be taking some solace in recent history, which suggests that it is seeing the cyclical nature of campaign giving, not an incipient rout. Obama aides point to Democratic Sen. John F. Kerry’s 2-to-1 advantage over George W. Bush at this juncture in 2004. The nominee challenging an incumbent enjoys a financial tailwind between the end of the primary season and the conventions, they said, scooping up contributors who sat out the primaries or “maxed out” in donations to other candidates.

And, like Romney, Kerry also benefited from a constellation of independent expenditure groups — left-leaning, in his case — that were angry about the first four years of the Bush administration.

Obama bundlers were circumspect in their comments Tuesday. “Look, big picture, it’s unquestionably a concern that they might be outspent by orders of magnitude by the super PACs,” said one bundler, who spoke on the condition of anonymity to be frank about the financial situation. But he added that as of Tuesday, he had not received any frantic new guidance from the campaign. “I’m not going to change what I do,” he said.

One Democratic strategist, a veteran of presidential campaigns, said Obama will need to focus his efforts on “donor maintenance,” which means schmoozing small groups of high-dollar contributors. The president has participated in scores of such gatherings, many of them at hotels within blocks of the White House, but he may need to do more.

“Obama is really going to have to put his energy into this in a way he hates to do,” the strategist said. “He hates that stuff. Clinton loved it. Hillary loved it.”

Amy Gardner, T.W. Farnam and Dan Eggen contributed to this report.