ENGLEWOOD, Colo. -- One minute the New Orleans Saints are cutting you and the next minute ... well, actually there were a lot of minutes when the New Orleans Saints were releasing rookie linebacker Todd Davis.

The Saints waived Davis in August, then again in September, then again in October and then again in November as he bounced between the Saints’ practice squad and the team's active roster.

“At that point you’re just trying to make sure you’re offering something that’s needed," Davis said. “You want to find a way to stay, it's like standing on the edge of something, you know, keeping your balance."

Then on Nov. 13 Davis, fully expecting to find himself back on the Saints' practice squad after being waived by New Orleans the day before, was the Denver Broncos claimed him. The Broncos saw potential special-teams help in the short term and had a wait-and-see approach about what Davis could do on defense, perhaps down the road.

Then Davis started appearing in some of the team’s passing-down personnel groupings in practice and this past Sunday in San Diego, with Brandon Marshall (left foot) and Danny Trevathan (dislocated left kneecap) having left what became a Broncos win with injuries, Davis was in the defense for 28 snaps (42 percent of the team’s total) and as the game drew to a close there were times when Davis was the only linebacker in the formation as Von Miller was lined up at defensive end.

Broncos head coach John Fox, who often preaches the mantra of "guys make their own roles," has said Davis showed he was intent on doing just that in his first month in Denver.

“I think he’s adapted quickly," Fox said. "He does have good football awareness and football character. I think he’s done a very good job in this short time."

"I just wanted to bring something to the team, special teams, backup on defense, whatever it was, do something positive," Davis said. "Bring something to the team every day … And I like to stay in my playbook a lot, I got a lot of help from the coaches one-on-one, trying to get prepared. I kind of felt a little bit overwhelmed at times, but I kept telling myself everything gets better with time."

Davis went undrafted last May after he had concluded his career at Sacramento State, not because of production -- he was a first-team All-Big Sky performer with a 131-tackle season as a senior. There was, however, the little matter of his on-campus pro day.

“Aw man, yeah," Davis said this week. "Think it was just me putting too much on myself, trying to do too much, trying to be too fast. I mean I’m out there running sprints the day before trying to be the best I can be and by the time I got to pro day my body was not there ... I was gassed."

And while most of the workout numbers were in line with others at the position, Davis' 40-yard dash time, depending on the stopwatch involved, was between 4.84 and 4.87 -- too slow for what most of the NFL’s decision-makers are looking for in a linebacker.

Which is why Davis' entry into the league came as an undrafted rookie with the Saints, who signed Davis on June 23 -- roughly a month before training camp opened.

“I think [the pro day workout] affected me, I really did," Davis said. "... But everything worked out so that’s kind of where I keep my focus now."

And with Trevathan having been placed on injured reserve Tuesday and with Marshall’s foot injury, Davis could very well find himself in the defensive mix again in the coming weeks. Marshall, who is the team’s leading tackler, left Qualcomm Stadium Sunday in a walking boot on his injured foot, but took to Twitter Tuesday night with a photo of himself wearing a shoe on his left foot, offering he had “graduated’’ from wearing the boot.

Marshall has been the every-down player at the position. Even if he returns quickly, Davis has still been one of the players who has worked in practice alongside Marshall at linebacker in some of the specialty packages, ahead of two other rookies in Lamin Barrow and Corey Nelson.

“It felt good [to come to the Broncos], it felt like home,’’ said Davis, a Palmdale, Calif., native who said he had 15 family members in the seats at Qualcomm Sunday. “It didn’t feel like I was coming in here as an outsider or anything like that … as soon as I got here it felt good … I just want to help find a way to make myself part of things. Whatever they want me to do, I’ll try to do.’’