The Republican party is no more eager to cut senior entitlements than is the Democratic Party -- they both use Medicaid and Social Security as political bludgeons, and neither side has made a serious proposal to cut costs.
You can try to turn this into a partisan political debate, but the bottom line is that both sides have a strong incentive to leave these programs alone (they benefit active voters). On the issue of entitlements, the primary practical difference between Republicans and Democrats is that the Republicans have a long history of attacking entitlements for poor people, in order to maintain the illusion that they care about costs.