Senate Democrats see New York Democrat Kathy Hochul’s win Tuesday night as confirmation that their public relations strategy on Medicare could help them ride to victory in 2012.

“I’m confident that Senate Democrats will be able to play offense in races across the country by remaining focused on the Republican effort to end Medicare in order to pay for an almost 30 percent tax rate reduction for the wealthiest Americans and big corporations,” said Sen. Patty Murray (D-Wash.), the chairwoman of the Democratic Senatorial Campaign Committee. “We’re not going to stop talking about this in states across the country.”

Medicare became a big issue in Hochul’s special House election in which she defeated the GOP candidate in a district that traditionally votes Republican.

Senate Majority Leader Harry Reid (Nev.) said the Democratic victory in a deep-red Republican district should give the GOP pause.

“The question to my Republican colleagues is basically, this, very simple. Will you listen to the American people? Because their message could not be clearer,” he said.

To help underscore the message, Reid has scheduled a Senate vote for Wednesday evening on the controversial House-passed budget blueprint, which calls for changing Medicare into a subsidy for private insurance. The House plan is expected to fail, but Democrats want to get Senate Republicans on the record as either supporting or opposing the Medicare plan.

GOP Senators, meanwhile, went one after another to the Senate floor to blast Democrats for failing to offer a budget plan of their own, which Republicans said was effectively a plan to let Medicare go bankrupt.

“Right now it’s on the road to bankruptcy and oblivion,” said Sen. John Cornyn (R-Texas).

Sen. Chuck Grassley (R-Iowa) accused Democrats of having an “ostrich” policy of sticking their heads in the sand and practicing demagoguery instead of working in a bipartisan way to solve the problem.