There are a few things that you might want to check here.
I was recently working on a campaign (still am actually) and the client had a landing page that had an insane bounce rate. After further investigation (I ended up installing Clicktale on the lander to get more insight) I found that people were actually clicking on his Call To Action, but because the page was so direct, and the Call To Action button created a popup on the page, it looked like the visits were bounces, when some of them were actually clicking through to the next page. Maybe you should check that out. If that is, indeed, the issue, then you may need to look into cross-domain tracking or just ensure that your google code is passing to the second page/step in your sales funnel.
Also, as other members have recommended, I would install or add in a mobile detection feature that can display the CSS that's going to show the page from a mobile standpoint, rather than the full desktop version. That amount of organic visitors on a daily basis is indeed enough to measure the quality of your landing page.
One more thing; Don't forget to try multi-variate testing your page.