I've seen a number of similar issues, but with no actual solution. Following http://docs.aws.amazon.com/elasticbeanstalk/latest/dg/create_deploy_Ruby_rails.html, I created a sample app without issue. However, I modified a few files, including the gemfile, ran bundle install, ran git add . && git commit -m "commit gemfile change"
Then, I ran git aws.push, received the following:
> c:\Users\mmoore\Documents\rubyapps\visitdaysaws>git aws.push Counting
> objects: 8, done. Delta compression using up to 8 threads. Compressing
> objects: 100% (5/5), done. Writing objects: 100% (5/5), 653 bytes,
> done. Total 5 (delta 3), reused 0 (delta 0) remote: To
> https://[secureurl]
> 091700..00005f 39eed5f98abacccccccccsaadeeeffa044354b740 -> master
c:\Users\mmatches\Documents\rubyapps\appaws>"c:\Ruby193\AWS-ElasticBeanstalk
-CLI-2.3.1\eb\windows\eb" status --verbose
Retrieving status of environment "appaws-env".
URL : appaws-env-dxf4aghrer.elasticbeanstalk.com
Status : Ready
Health : Green
Environment Name: appaws-env
Environment ID: e-123abz4rpw
Solution Stack: 64bit Amazon Linux running Ruby 1.9.3
Version Label: git-39eed5f98abacccccccccsaadeeeffa044354b740-1363313513
78
Date Created: 2013-03-15 13:48:56
Date Updated: 2013-03-15 16:34:00
Description: None
RDS Database: AWSEBRDSDatabase | aa1adfga3tfa2a.cadfef60egmm.us-east-1.rds.amaz
onaws.com:3306
Database Engine: mysql 5.5.27
Allocated Storage: 5
Instance Class: db.t1.micro
Multi AZ: False
Master Username: ebroot
Creation Time: 2013-03-15 13:54:20
DB Instance Status: available
Despite this, I still receive the generic Welcome message:

I've checked the size of my git repo and it's larger than the default app, but only 6.5 MiB. I've also tried pasting in core files, no change. I'm open to any ideas at all.
Update
Ran the suggested remove file, still received the general page, but when navigating to index.html (which theoretically is not there), you can see the application load or attempt to load via an error.