The deadline to franchise players was Monday at 4 p.m. ET.
Spencer's agent, Roosevelt Barnes, spoke with team officials twice in the last two weeks in an attempt to forge a new contract for the former 2007 first round pick from Purdue.
Barnes, said the two sides will continue to talk about a long-term deal despite the franchise tag.
Spencer has until July 16 to sign the tag and isn't in a rush to sign it at this moment.
"There's a lot of different ways to handle the business of the NFL and the franchise tag is one of the ways teams can try and keep their really good players," coach Jason Garrett said Monday night after co-hosting a charity event at a Dallas-area high school. "Spencer is a guy who has played really well for us and is the right kind of guy, been a very productive player for us.
"A lot of people get caught up in he only has six sacks and I think if you look at his total production, how he's effected quarterbacks, how he's effected games, tackles for loss, hurries, tackles all of that stuff, he's really been a strong contributor to our football team."
In five NFL seasons, Spencer, 28, has 266 total tackles and 21.5 sacks. He also has 10 forced fumbles and 10 pass breakups.
He's been compared, almost unfairly to his fellow outside linebacker DeMarcus Ware, who is a seven-time Pro Bowler and has 99.5 career sacks.
The Cowboys value Spencer's ability to stop the run and drop him back in pass coverage more often than Ware, which leads to fewer sacks and quarterback pressures.
Yet, Spencer has had stretches where he doesn't get any sacks at all. He started the 2011 season with three sacks in the first three weeks of the season but didn't get one the last four weeks. The Cowboys coaching staff did however credit Spencer with seven quarterback pressures the last four weeks.
The Cowboys can still work out a deal with Spencer as they've done with players they've franchised in the past. Safety Ken Hamlin and left tackle Flozell Adams were given the franchise tag by the organization but later worked out long-term deals.
Cowboys officials have only franchised three players: Adams, Hamlin and Spencer.
Calvin Watkins covers the Cowboys for ESPNDallas.com.