With an easier schedule over the next 6 weeks and improved play, the Jags seem like a threat to win at least one more game this season. Assuming that the Jags will finish with at best a 4-12 season (with wins over Cleveland, Buffalo, Houston, and Tennessee), this post will look at the teams that seem most likely to challenge for the #1 pick .
1. Tampa Bay Buccaneers (2-8)
Looking at that remaining schedule it seems rather likely that the Buccaneers are guaranteed 4 losses: @Lions, @Panthers, @Saints, and VS 49ers. The Rams also seem pretty likely to beat the Bucs, seeing as the Rams are essentially the Colts minus Andrew Luck. The Bills game is more of a toss-up, but as the game is in Buffalo, the Bills should be able to pull that one out. Projected finish: 2-14
2. Atlanta Falcons (2-8)
The Falcons are falling apart and have looked horrible the past couple of weeks. It seems likely that the Falcons will drop games to the Saints, 49ers, and Panthers. I think it is likely that they will lose to the Packers regardless of if Aaron Rodgers suits up or not (though they would have a chance if Scott Tolzien were to start). @Bills and VS Redskins are likely to only winnable games left for the Falcons, but with both games being outdoors in cold locales, the Falcons could drop those games as well. Projected finish: 3-13.
3. Minnesota Vikings (2-8)
The Vikings probably loose the Ravens, Eagles, Bengals, and Lions games, but have a chance against a Rodgers-less Packers (almost everyone does) and the Bears (horrific run defense, which plays to the Vikings strength). Projected Finish: 3-13.
4. Houston Texans (2-8)
The Texans remaining schedule is split between good teams (Patriots, Colts, Broncos) and bad teams (Jaguars twice, Titans). The Broncos and Patriots games are as close to assured losses as you can get. The Colts however have shown that they only care about getting up for the better teams in the league and could be a trap game for the Colts (they play KC right after Houston). I think that the Texans are likely to split the Jags games and probably win versus the Titans, though they could just as likely lose all three. Projected Finish: 3-13
Obstacles to getting Bridgewater:
Should the Vikings or Buccaneers end up with the first overall pick, they are probably going to take a quarterback (probably Bridgewater, unless they like Mariota's ceiling over Bridgewater's polish). If the Falcons or the Texans end up the first overall pick, things get a little more interesting.
The Falcons don't need a quarterback (gave a mister contract to Matt Ryan) but may decide to trade away the chance for Clowney to get more draft picks (to make up for the holes that the Julio Jones trade left them with). They could also decide that the Clowney is indeed a once in a generation pass rushing prospect and select him (they are lacking in the pass rushing department). Ultimately I think that the Falcons will try and get more draft picks, especially since this draft is one of the deeper drafts in memory (with talented pass rushers as Anthony Barr and Vic Beasley projected to be available in the early teens).
For Houston the last six games will determine if they decide to draft a quarterback with the #1 pick (if they get it). Keenum has been playing well, but the new regime (there will be a new regime) will probably want to start over with their 'guy', and hence select Bridgewater/Mariota.
What I think this means for the Jags
I think the Jags are still the favorite for winning the Bridgewater/Clowney sweepstakes, even though there improved play and easier schedule set them up for a couple of winnable games. Regardless of if the Jags get the first pick or not, this deep draft should provide the Jags with enough talent to start competing for the division in the seasons to come.