Isn't that funny? That's exactly what was siad about the new Republican Party about 150 years ago.
How many moderates and swing voters are going to vote for a doctrinaire conservative presidential candidate? Especially one that has not one but two major parties and their resources being levied against them?
It ain't impossible but this candidate would need at least $1 billion (probably a lot more would be needed) to take on both parties machines and their established campaign infrastructure and voter biases.
The best shot any conservative third party would have at truly having influence would be to focus on winning seats in the house and senate. Now after a few election cycles when the party has an established presence in congress, a more experienced campaign machine, and enough time for voters to see the party as not an overnight sensation but a real political force then it might be possible to run a Presidential Candidate. But they still would need a boat load of cash.