WASHINGTON — Amplified by the right-wing message machine, Republicans paint President Obama as an unyielding left-winger, an unreconstructed liberal who refuses to compromise. The president’s critics have turned the truth inside out: One of Obama’s greatest political weaknesses has been his stubborn — and unrequited — love for bipartisanship. The president has made some of his biggest mistakes trying to woo a GOP opposition that has committed itself to frustrating him at every turn. If he had ignored recalcitrant Republicans, for example, his health care legislation might have become law without months of damaging political drama. In an interview last...