Republicans will almost certainly reject that, refusing to vote against this middle class tax cut unless the tax cuts for the wealthiest Americans are also extended. They will be rejecting the only viable path for extending the cuts for the middle class: the Senate has already rejected extending the tax cuts for the rich, and won't pass the House bill.
The Republicans won't just be voting against working families, they'll be voting against their own political interests, Today's Quinnipiac University/CBS News/New York Times of critical swing states shows that once again:
But for Republicans, voting with Grover Norquist comes before voting for the interests of their constituents. Don't expect that to change with today's vote.