“Is there a way to win the hearts and minds of ObamaVoters?”
No. Of course not.
There is as much possibility of doing that, as there is of convincing conservatives to vote for the ‘rats, and for what the ‘rats represent.
The two sides hold worldviews so far apart, that short of a few “total self-conversions”, the gap can’t be bridged. It’s not so much that the right has moved “further right” (conservative positions don’t change much), it’s that the left has moved far beyond the boundaries of what even traditional democrats once considered normal.
And the left will keep moving leftwards. What will it look like 20 years from now?
If you have an aquaintence whom you know to be voting for Obama, try asking them to convince *you* to vote for Obama. Try to do it without having your mind made up in advance. Listen to their arguments, but be armed with facts in reply. Offer those facts cordially.
A conservative ought at least yield the point there is some place for government to provide food and shelter for those who literally have no means to contribute to the GDP. Some people are born with physical maladies or other weaknesses, and sometimes working people do not have all it takes to support them.
A conservative should never yield that killing unborn citizens is a matter of convenience or personal choice.
Between those matters there is much room for debate. But it does not help to assume all Obama voters are totally unreasonable, just as it does not help for them to assume the same of you.
In short, invite them to convince you, but don’t play games. Listen first.