Why not start your press releases with a ‘TwitterCue’, i.e. a 140 character line which sums up the content? Done properly (and without undue abbreviations), this sounds like a good habit for PRs to get into.
Not only would it work well for social media optimised press releases and those distributed to bloggers, citizen journalists and through PR Newswire (and similar services – it would be excellent if ‘Tweet this’ links also brought up the TwitterCue rather than just the headline), but I’m also sure it would be useful for time-pressed journalists.
The only problem I can see on embargoed press releases would be linking through to a live website at the end of the Tweet. But I suppose public relations-savvy organisations will have their latest news stories on the home page anyway and so a link to the main URL should suffice.