WASHINGTON — President Trump’s repeated threat to declare a national emergency so he can build his border wall without congressional approval has been denounced by Democrats as extreme and an overreach. But it could be the only politically realistic way out of the shutdown crisis in the nation’s capital. “ I think we might work a deal, and if we don’t, I may go that route . I have the absolute right to do national emergency if I want,” Mr. Trump told reporters on Wednesday. “ My threshold will be if I can’t make a deal with people that are unreasonable.” If the president does invoke emergency powers to circumvent Congress, it would be an extraordinary violation of constitutional norms — and establish a precedent for presidents who fail to win approval for funding a policy goal. But Mr. Trump’s threatened move offers both sides a face-saving solution in the budget standoff between the president and congressional Democrats that has prompted a partial government shutdown