No, I would not eliminate either party.
But I would rigorously enforce the Constitution as written.
Including the 10th amendment, which forbids the Fed from exercising any powers not explicitly given to it by the Constitution. Bye-bye to 3/4 of liberal spending on non-listed programs.
And the so-called "Welfare Clause", which in actuality limits any Federal spending to only programs that benefit all Americans. Bye-bye to spending for Special Interest groups and "redistribution of wealth" programs.
And the 2nd amendment, which says that since freedom is necessary, no govt can have any say in who is or is not allowed to own and carry guns etc. Bye-bye to the Left's most cherished scaremongering, and hello to fear criminals will feel before the mug or rape someone, knowing that there's probably someone in the crowd who's armed and ready.
The Democrat party (and liberals in the Republican party) will thereby lose most of their reason for existing in their present form.
But if they want to go on existing anyway, that's OK with me. They'll just find no support and no legal basis for doing what they presently do.