That’s not going to work the way that you want it to. If googles search bots continually see the date changing on that page they’ll flag it and look at it very critically to determine just why the date published is different every time they index the page. They’ll also flag questions about the incoming links ot the page – how could a page have links to it from a few weeks ago when the date says that it’s only a day old? Those sort of questions that there’s no reasonable answer to has a very good chance of hurting that page long-term.
There’s no SEO advantage to having something listed as “2 days old” in the search engine results. You’re more likely to get better results by having that page up and running for a longer time. It will seem like a more authoriative page rather then something that’s just been thrown up now.
If you are really worried about this (but there’s no reason to be) you would be best off editing your template files to remove the date that it was posted. That way that information won’t be shown and there won’t be any of these issues.