Good question. Short answer: Yes. But the GOP has to start acting like Republicans to do it.
In many respects we already are the party of the people. The GOP has 40-60% of the country ideologically, depending on the issue. What we need is to quit balkanizing ourselves through factional identity infighting between libertarian conservatives, social conservatives, fiscal conservatives, pro-defense conservatives, pro-business conservatives - something our opponents promote heavily, by the way, and use to isolate us - and focus on the big picture with which we all agree.
And, we need to learn to grow a pair. Fighting for what you believe in is no fault.