WASHINGTON  President Obama on Wednesday made note of his setbacks as well as his victories in the surprisingly productive lame-duck Congress, and served notice that he would resume the fights on immigration, spending priorities and more when the new Congress with its Republican reinforcements convenes in January.

“One thing I hope people have seen during this lame-duck: I am persistent,” Mr. Obama said, with a flash of energy, at a valedictory news conference. “If I believe in something strongly, I stay on it.”

Many in his party, especially liberals, have openly questioned just that  how strongly Mr. Obama holds his beliefs and how willing he is to fight for them.

Earlier on Wednesday, Mr. Obama was able to dispel such doubts on one issue when he signed a measure repealing the 17-year-old “don’t ask, don’t tell” policy against openly gay people serving in the military.