GOLF WITH THE PRESIDENT ... at least, that was the case for Dallas Cowboys legends Emmitt Smith and Tony Romo, who bailed on watching Tiger to play 18 with Barack Obama!!

It all went down somewhere in Texas this weekend ... when Emmitt, Romo, Barack and former Dallas mayor Ron Kirk hit the links for a round of golf.

Unclear who in the foursome took the win ... but odds favor Tony -- who's so good, he's set to play in next month's AT&T Byron Nelson Tournament with PGA pros.

As for ditching El Tigre ... don't worry -- seems the guys made it back in time to catch his unbelievable Masters victory, with Obama personally congratulating the golf legend.

"To come back and win the Masters after all the highs and lows is a testament to excellence, grit, and determination."