This, of course, does come with a caveat. If you did this you would still have to face your voters at home. They would still get to express their displeasure at taking away their right to vote. They would still get to express their displeasure at so perverting the electoral process that a candidate decisively beaten in the popular vote still made it to the White House. You would have to deal with the fact that your Republican Party is not republican at all because republics are based upon the notion of sovereignty resting in the hands of the people and your actions directly, and significantly, impacted upon that sovereignty.
So, go ahead, Republicans. Embrace the naked power grab. Maybe you'll squeeze an election out of it, but that's about it. It'll eventually happen that a Democratic candidate will win the popular vote by a comfortable margin, and also would have won the electoral college, but for your shenanigans, and then the gig would be up. Your party would be destroyed and, with it, the electoral college system would most likely go as well. Maybe it wouldn't formally go at first because of how difficult it would be to amend the Constitution to that effect. However, de facto abolition would likely occur quickly. That, in turn, would likely lead to formal abolition in order to better manage the popular vote system established through the same mechanism you are currently considering.
Good luck, Republicans. You think you're pulling a fast one now, but I assure you that we'll be the ones that get the last laugh.