“We’re not going to have 60 votes,’’ said McConnell, who has developed a reputation as a shrewd political strategist and master of arcane Senate procedure. “It is important to remember Barack Obama will still be president for two more years, and the veto pen is a powerful thing. So we need to be realistic.”

McConnell’s task would be a daunting one, trying to attract the Democratic votes he’ll likely need to advance bills without having defections from his own camp. Hard-line conservatives are likely to insist on a renewed fight to repeal the president’s healthcare law and to make spending cuts to balance the budget. Social conservatives would push for new legislation to restrict abortion and benefits to same-sex couples.

As majority leader, McConnell would command significant authority in setting the agenda. But in a speech in January he indicated that he would aim to focus on areas of consensus, not solely conservative priorities — like repeated votes to repeal Obamacare.

“There’s a time for making a political point, even scoring a few points. I know that as well as anybody,” he said then. “But it can’t be the only thing we do here.”