The GOP plan, written by House Budget Committee Chairman Paul RyanPaul Davis RyanGOP leaders pitch children's health funding in plan to avert shutdown Lawmakers see shutdown’s odds rising Fix what we’ve got and make Medicare right this year MORE (R-Wis.), would give seniors payment support for health insurance plans. Democrats' portrayal of the plan as a threat to the longevity of the popular program has resonated among seniors in particular.

Reid also said it was a contradiction that Republicans were pushing to preserve billions of dollars in tax credits to the oil industry last month while simultaneously supporting the Ryan plan that would cut $5.8 trillion in spending over 10 years.

“It appears clear they would rather balance the budget on the backs of seniors,” said Reid on Tuesday, repeating a line popular among Democratic lawmakers. “Protecting seniors on Medicare is our top priority.