Their shame will not be felt because the kind of Republicans who are in office now (the moderates having been long ago thrown out) have no shame. But they can feel the hatred and loathing that loyal Americans have for treasonous activities, loyalty to despots and those who help thieves like Trump. 
When the Republicans begin to dismantle Medicare, Medicaid and Social Security they will finally be seen for what they are: violent criminals. The response of the American majority, of those who are loyal to our country and democracy, should be commensurate with the heinousness of the treason and thus terrible.