Republican proposals for Medicare center around the use of a voucher system, where the government issues vouchers of predetermined value for the purchase of private health insurance. The idea is that a voucher system would simplify the amount the government disburses to Medicare recipients and would make long term cost analysis easier as fewer variable rates of expense are easier to account and track.
On the income side, Republicans would lower all marignal tax rates by 20% across all income levels. For those unfamiliar, the United States employs a progressive income tax, which taxes at an increased rate at higher levels of income accounting for deductions. As an example of how the tax is calculated see here. In 2011, the tax rates and income threasholds were thus:
A 20% reduction in these rates would mean that individuals earning less than $35,350/yr in gross annual income would incur no federal income tax, while those earning $35,351 and higher would only be subject to a maximum rate of 15%. Married couples filing their taxes jointly wouldn't pay tax on the first $70,700 of their gross annual income and individuals filing as Head of Household wouldn't pay tax on the first $47,350.
Republicans also want to repeal the Alternative Minimum Tax. The AMT is the second of two federal income taxes that U.S. wage-earners may be required to pay. According to U.S. tax code, a person must either pay the AMT or the Marginal rate based on whichever amount would be greater in accounting for possible exemptions. Overall, the AMT levies a fairly flat rate (though the percentage is considerably higher) and uses a predetermined amount for exemption based on income. The AMT was originally intended to target high income individuals as the rates on captial gains (which they're more likely to have) and regular income are higher, while the amout retained through exemptions is phased out to zero at the highest levels of income.
2012 AMT Tax Structure:
Lastly, Republicans want to cut corporate tax rates to a maximum of 25%. Similar to individual income taxes, corporate taxes in the U.S. are also progressive so higher levels of income are taxed at higher rates.