Don't Fight: The president shouldn't cave, exactly, but his first job should be to show voters that he hears them. So he'll heed the polling that shows the vast majority of the public wants cooperation. This is the core of why people liked him in 2008, and if he is going to recapture that constituency, the president has to remind people why they liked him in the first place. As the president has said, Obama lost independents and moderates because he took so many emergency measures, it looked like he was bent on expanding government. If he spends some time at least looking like he's willing to work with the party associated with shrinking government, then he can help correct that perception. And then if he ultimately does have to fight more overtly, he can at least say that he tried to cooperate.
If you did not find the argument your family is having in the above list, there is one failsafe measure that you can apply to engage a dearly loved rival holding forth during the meal. "What proof do you have," you might ask, after they make their strongest claim. Often you will find that towering opinions are based on nothing more than a gut feeling. You can then point out that if they want to proclaim on the strong messages they're receiving from their stomach, the best way to do so is to thank the host.
AP Video: President Obama Pardons a Turkey