WASHINGTON — Donald Trump and Mitch McConnell reaffirmed their alliance of necessity Monday in a raucous Rose Garden news conference that also underscored their sharp differences. The garrulous president claimed they were longtime friends now closer than ever; the reserved Senate Republican leader allowed that they share goals and speak often. It was a spectacle that mesmerized Washington, as Trump and McConnell appeared side by side for more than a half-hour, the president tossing off answers — sometimes mini-speeches — on all topics while McConnell, disciplined as always, delivered brief, scholarly explanations about the legislative process and the risks to their party of nominating candidates who can’t win. At various points, the president denounced the Russia-Trump campaign investigation, lauded himself for his record on judicial nominations, argued wrongly that “it took years for the Reagan administration to get taxes done,” and claimed that past presidents hadn’t necessarily contacted bereaved family members to mourn lost service members — before backtracking on that assertion when pressed.