Google often does Webmaster Central Hangouts on Google+. This gives webmasters an opportunity to connect with Googlers and learn valuable tips about how they can get more out of their sites, and out of Google.
Google's Pierre Far announced a couple of upcoming hangouts for Tuesday, March 27, and Wednesday, March 28. Both begin at 2PM UK time, and last for an hour. Far writes:
US-based webmasters: please be careful with the time difference for these as Europe would have switched to summer time by then!
Topic: Anything webmaster-related: Webmaster Tools, Sitemaps, crawling, indexing, duplicate content, websites, web search, etc.
To join, you obviously need a Google+ account. The thing is, they're only limited to 10 participants, but people tend to come and go, so even if you can't immediately get in, you might be able to squeeze in sometime within the hour. It's a chance to get some direct advice about your site from Google, so depending on how pressing your issue is, it may be worth waiting to get in.