"The law recognizes a difference between a true threat - one that can be carried out - and the reported racist rantings of a drug addict," U.S. Attorney Troy Eid said.
He said the men's plans were "more aspirational, perhaps, than operational."
The three have been charged with drug and weapons offenses but not with threatening to assassinate Obama or with other national-security-related crimes.
Obama will become the first black nominee for president by a major party at this week's convention.
An affidavit released by Eid's office Tuesday showed the investigation into alleged threats began with an unnamed female who was with the men - Tharin Gartrell, 28; Shawn Robert Adolf, 33; and Nathan Johnson, 32 - while they were doing drugs in a Denver hotel room last weekend.
The woman told police that the men were calling Obama the N-word and saying he shouldn't live in the White House.
Adolf and Johnson made similar racist statements to police, but Eid said authorities determined there was no firm plot to harm Obama.
"A bunch of meth heads get together, we don't know why they do what they do. ... People do lots of stupid things on meth," Eid said. "If you're talking about a true threat, there has to be some evidence they're not just talking about it or thinking about it, especially in a drug-induced state."
Johnson told a Denver TV station that others involved in the case had made racist statements regarding Obama and had discussed killing him Thursday, the day of his acceptance speech at Invesco Field at Mile High.
"He don't belong in political office. Blacks don't belong in political office. He ought to be shot," Johnson told KCNC-TV Monday in a late-night interview from jail.
When asked whether he felt there was a plot to kill Obama, Johnson said, "Looking back at it, I don't want to say yes, but I don't want to say no." He said he wasn't involved in any plot.
By Tuesday, Johnson was declining media requests for interviews. He did not speak at a bond hearing where he was given $10,000 bond.
Gartrell was arrested after police in Aurora, a suburb east of Denver, stopped a truck that was swerving erratically around 1:30 a.m. Sunday. He had a suspended driver's license and the truck was rented in the name of another person, said Aurora police Detective Marcus Dudley.
Aurora police Lt. Bob Stef said police saw two scoped rifles, two wigs, camouflage clothing, a bulletproof vest and two walkie-talkies in the truck. A search also revealed 4.4 grams of what police believed to be methamphetamine and three IDs in other people's names, Stef said.
Johnson and Adolf were arrested in area hotel rooms after interviews with Gartrell. Adolf jumped out a sixth-story window of a hotel when police arrived Sunday. He broke his ankle in the fall but tried to run before police found him a short distance away.
Adolf was charged with possession of a firearm by a convicted felon, possession of body armor by a violent felon and possession of methamphetamine with to intent to distribute, according to a criminal complaint filed Tuesday in U.S. District Court in Denver. Gartrell and Johnson were charged with simple possession of meth, meaning the amount involved was less than 5 grams, and Johnson also was charged with possession of a firearm by a convicted felon.
Three senior FBI officials said it's unclear whether shooters could have had a clear path to hit the stage from outside the convention hall. At least two of the men may have had white supremacist ties, the officials said, adding that it was unclear whether any of them were serious about carrying out threats. The officials spoke on condition of anonymity because they were not authorized to discuss the case.
A fourth federal official familiar with the investigation said an assassination attempt was unlikely.
"The capability and their opportunity and what they had for their weaponry - I don't see that they would have been able to carry it out," the official said on condition of anonymity because the investigation is ongoing.
Adolf was hospitalized and was being held on $1 million bond for several outstanding warrants involving drug charges. Adolf had a handcuff key in one hand and a swastika ring on the other when he was arrested, a senior FBI official said. Adolf was listed on the "Most Wanted" list of the Weld County, Colo., sheriff's department for burglary, larceny, aggravated motor vehicle theft and other charges.
Gartrell, who has no known address, was being held at the Arapahoe County jail on $50,000 bail on drug and weapons charges. The jail said he was due in court Thursday.
Eid would not describe the woman who was allegedly doing drugs with the men or say whether she was charged with a crime.
Law enforcement officials were also investigating whether the men were linked to vandalism shootings that targeted at least two federal buildings in Denver over the past two weeks. Windows were shot at the U.S. Custom House and the U.S. Military Entrance Processing Station on the same street in Denver's downtown Federal District.
Additionally, a bullet was recovered from a Hertz rental car that was hit on Aug. 15, and authorities are now looking to see if it could have matched the guns seized from the men.
Gartrell lived in rural Nevada in the 1990s with his father, a journeyman ranch hand and heavy equipment operator, Lincoln County Sheriff Kerry Lee said Tuesday.
Lee told the AP that Gartrell was run over by a truck as a child and that "it was absolutely amazing that he wasn't hurt badly."
As a teen, Gartrell tried to enroll at a high school about 80 miles north of Las Vegas, but provided transcripts from a high school in Colorado that showed "quite a bit of disciplinary action," said Debi Smallwood, administrative aide to school Principal Steve Hansen. Gartrell was told he'd have to enroll in an alternative high school but never did, Smallwood said.
