ORLANDO, Fla. — Americans for Prosperity, the Tea Party organization backed by the Koch brothers, is set to begin a $25 million advertising assault aimed at President Obama, its largest effort to date.

The ad campaign is the latest example of how independent political groups funded by a small number of wealthy donors are shaping the presidential campaign in key swing states. Conservative groups and “super PACs” have been particularly aggressive, pummeling Mr. Obama on the airwaves as Mitt Romney’s campaign waits until after the Republican National Convention — when it will be legally permitted to spend the hundreds of millions of dollars it has raised in recent months — to ramp up its advertising efforts.

American for Prosperity said that the first of several ads would begin appearing on Wednesday in 11 battleground states, including here in Florida. The campaign will last for three weeks — extending through Labor Day weekend — and includes Colorado, Iowa, Minnesota, Nevada, New Mexico, North Carolina, Ohio, Pennsylvania, Virginia, and Wisconsin.

The first ad, titled “President Obama: A One-Term Proposition,” hits the president over the rising national debt — an issue that conservative political groups like Americans for Prosperity and American Crossroads, which is run with the help of Karl Rove, believe is particularly powerful with swing voters in this election.

The commercial focuses on an excerpt from an interview Mr. Obama gave to NBC News at the beginning of his term in which he pledged to cut the debt. It was during that interview that he uttered the phrase that his rivals now regularly use against him: “I will be held accountable.”

The Obama administration has faulted the Republicans as failing to reach a budget deal to help close the deficit, saying the party’s opposition to raising revenues through higher taxes and by closing loopholes is the main reason more progress has not been made on this front. Democrats also note that when President Obama came into office, he inherited a growing budget deficit from President Bush.

The ad takes a relatively straightforward approach, avoiding hyperbole or over-the-top negativity. An image of the national debt clock appears on screen for much of the ad, ticking ever higher. It ends with Mr. Obama’s words, “If I don’t have this done in three years, then there’s going to be a one-term proposition.”

The ad goes a step further than Americans for Prosperity’s previous knocks against the president. Those ads focused on specific policies of the Obama administration like energy, an important distinction under campaign finance rules. This new ad campaign will take aim directly at the president, forgoing the issue ad approach but perhaps opening the group up to greater scrutiny.

The group is a tax-exempt organization whose ads must be primarily issues-focused, although the efforts of such groups have faced increasing scrutiny by advocacy organizations who accuse them of treading into overtly political activities.

This campaign is the first time the group has expressly advocated for Mr. Obama’s defeat in an ad. “We don’t take this lightly,” said Tim Phillips, president of Americans for Prosperity. “We’ve always stayed away from express advocacy. But given the president’s disastrous record, we felt this was necessary.”

Subsequent ads in this campaign will feature the personal stories of Americans who have been hit hard by the economic collapse, Mr. Phillips added.

Campaign finance experts noted that by taking direct aim at the president in their ads, Americans for Prosperity was taking advantage of a legal loophole that allows it to keep the identities of its donors secret.

“If the organization had continued running ads attacking Obama without containing express advocacy they would have had to disclose all their donors dating back to the beginning of 2011,” said Fred Wertheimer, president of Democracy 21, which fights for greater campaign finance transparency.