According to ESPN's poll of NBA columnists, the Blazers are the sixth best team, following the Lakers, Cavs, Celtics, Magic, and Spurs. These are the teams that have played in the finals for the last 3 years. So the Blazers are expected to be the best team that hasn't played in the NBA finals since 2007.
Since these teams have been competing at the highest level for several years, they are somewhat older than the Blazers. Let's look at the ages of their core five players in three years to see how we stack up at that time.
Lakers: 24 (Bynum), 32 (Artest), 32 (Gasol), 34 (Kobe), 38 (Fisher). Kobe would be past prime but still potent, Gasol and Artest would be declining, Fisher would be out of the league. Only Bynum would be young, entering his prime, and a likely all-star.
Cavs: 27 (LeBron), 29 (Williams), 29 (West), 29 (Varajao), 40 (Shaq). LeBron would be at his MVP peak, with all but Shaq in their primes. Shaq would be retired.
Celtics: 26 (Rondo), 27 (Perkins), 34 (Pierce), 36 (Garnett), 37 (Allen). Allen and Garnett would likely be out of the league or bench specialists, with Pierce past prime but still potent. Rondo -- likely all-star -- and Perkins would be in their primes.
Magic: 26 (Howard), 27 (Bass), 30 (Nelson), 33 (Lewis), 35 (Carter). Carter and Lewis would be declining, with Howard -- leagues top center if Oden isn't -- Bass and Nelson in their primes.
Spurs: 30 (Parker), 32 (Jefferson), 35 (Ginobili), 36 (Duncan), 38 (McDyess). Duncan, McDyess, and Ginobili would likely be out of the league or bench specialists. Parker and Jefferson would be late prime.
Blazers: 23 (Batum; or 25 Webster), 24 (Oden), 27 (Aldridge), 28 (Roy), 36 (Miller). Oden and Batum/Webster would just be hitting their primes, while Roy and Aldridge would be in their early primes. Miller would be out of the league or a backup specialist.
So the Blazers -- with Roy, Oden, Aldridge, and Batum/Webster all in their primes -- would face the Bynum/Old Kobe/Old All Star Lakers, the LeBron plus three in their prime OK but not great sidekicks Cavs, the Rondo/Perkins/who knows who else Celtics, the Howard/Nelson/Bass Magic, and the Parker/Jefferson Spurs. Of these teams, the Cavs and Magic would be the biggest competition, with the others a good bit behind.
So the prospects for a Blazer dynasty are pretty good, when compared with the recent playoff finalists. Go Blazers!