Making authenticated calls to Twitter can be a pain.
Make sure that the parameters in your signature base string are ordered alphabetically.
Take this:
oauth_consumer_key={consumerkey}&oauth_nonce={nonce}&oauth_signature_method=HMAC-SHA1&oauth_timestamp={timestamp}&oauth_token={token}&oauth_version=1.0&status={tweet text}
fill out the values, encode it in Base64, and then put it together like this:
POST&{base64 encoded url}&{base64 encoded base string}
this will be the string you need to sign (without the brackets). (The url in this case will be https://api.twitter.com/1.1/statuses/update.json)
The signing key needs to be built like this:
{consumer secret}&{token secret}
The signature is a HMACSHA1 hash, which is then base64 encoded.
Then you need to put this in the Authorization header:
OAuth oauth_consumer_key="{consumer key}",oauth_nonce="{nonce}",oauth_signature="{signature}",oauth_signature_method="HMAC-SHA1",oauth_timestamp="{timestamp}",oauth_token="{token}",oauth_version="1.0"
And finally put status=your tweet text
as the posted data in your request.
I hope this helps.