"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 saidund 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.