Here's a little clarification on what BB has stated repeatedly in the media, and how it is being played in discussions when it comes to UFAs such as Kovalchuk.
Brian Burke is not against long contracts
Brian Burke is not against top money
Brian Burke will not give out NTC (other than extenuating circumstances)
BB has said on multiple occasions, that if was in Pittsburgh or Washington, he would have no problem signing CrOvMal to the kind of deal that #8 got: 10+ years at max dollars.
But he has said repeatedly that you gotta be pretty confident that the player you are signing is in that stratosphere. If you aren't, then you will get hamstrung with an overpaid player for a lot of years. If the current "bad" contracts of the NHL were only 3 or 4 years in length, they would not be so crippling to their teams and immovable for their respective GMs (See: Campbell, Huet, Drury, Gomez, Briere, Redden, etc, and even Vanek in some respects).
What Burke is against is the idea that you can bend the cap hit to your favour by drawing out these long contracts to the point where the player may no longer be NHL-competitive, with the hope/understanding that a retirement will erase the final years of the contract around 38, 39, 40 years old. The player will only forfeit a pittance of 500k to 1m in most cases, as these kinds of contracts are all very front-loaded. Any kind of wink-wink deal to get and old guy off the books is a contravention of the CBA in his opinion.
In the Kovalchuk situation, I think Burke sees that Ilya is not the integral piece they need. As a 90-100 pt offensive superstar winger, he fills a hole that is not necessarily the weakness of the Leafs. If Kessel can be a 35-45 goal player, putting up ~80 pts a season, you are just loading up at a redundant position.
Therefore, to weaken his salary freedom by committing max dollars to a player that isn't going to have the max impact on this team, it probably gives him pause to offer more than 5 or 6 years for Kovalchuk. If this is a year ago though, and the Leafs don't have Kessel yet, I think Toronto would be very much in play to sign Kovalchuk. Imagine if Nash and Kovalchuk had become available last summer, I don't believe for a second that Burke would have hesitated to offer either of them a 7-8 year deal.
You would love for Kovalchuk to give the Leafs a 1-2 punch of Kovy and Kessel, similar to Ovechkin & Semin in Washington, but Toronto doesn't have any sure-fire star centres in the mix and they still have big question marks in net. If we already knew that Kadri was the second coming of Yzerman or Francis, yeah, it would be a possibility to bring in a top winger to try and bludgeon teams to death come
Toskala hell or high water.
But until Burke has a very good idea of what his team actually is (not the rotting cadaver of the Ferguson errors + Fletcher hatchet job), it would not be prudent to commit to a player that is not your biggest weakness.