The U.S. Senate voted down a Republican budget plan Wednesday, which included Wisconsin Rep. Paul Ryan's blueprint to reform Medicare.

Some liberals argue that voters are scared by the Republican plan. They say a special election in New York this week proves it.

Democrat Kathy Hochul beat a Republican and a third-party candidate in a special election in one of New York state's most conservative congressional districts.

Many political analysts say her victory may have come down to one key issue.

"Republican Jane Corwin supports a budget that essentially ends Medicare," one analyst said.

Ryan's budget plan, which reforms Medicare in the long term, does not impact Americans 55 and older today. It reduces Medicare's cost by eventually replacing the system with one where seniors would buy government-subsidized private insurance.

"I think the New York 26th tells Republicans that the end of Medicare is bad policy and bad politics," Rep. Steve Israel, D-N.Y., said. 

Republicans blame Tuesday's election loss on the third party candidate, who they say drained support from their candidate.

But Democrats claim the special election is proof that voters are worried about Republican plans to reform medicare.

When the Ryan budget, including the Medicare reform plan, came up for a vote in the Democratically controlled Senate on Wednesday, all of the Democrats, as well as five Republicans, rejected it.

Ryan defended his plan Wednesday at a meeting on the federal budget.

"You may not like the plan, but it fixes the problem. It gets the debt paid off. It balances the budget," Ryan said.

On the very same stage, former President Bill Clinton criticized it.

"I applaud Congressman Ryan for making a suggestion. But I think on the merits, it doesn't work," Clinton said.

Still, the former president whispered some surprising support for the Republican when the two met backstage.

Clinton even offered to talk more with Ryan later because both men agree something has to be done.