“We are going to use the budget to prove to Americans that every time Republicans choose to protect oil company profits while privatizing Medicare for seniors, seniors will chose Democrats,” Mr. Israel said.

He and other party strategists say they believe the Republican stance on Medicare could be particularly persuasive against incumbents in states like Florida, Illinois, Michigan, New York, Ohio and Pennsylvania. It could carry extra potency, they say, because Republicans hit Democrats hard in the 2010 midterms on cutting Medicare as part of the new health law and Democrats now intend to turn that message back on them.

President Obama is expected to enter the debate over entitlement spending in a speech on Wednesday and could offer his own views on how to control Medicare costs. But he is expected to go nowhere near as far as Republicans did in the Ryan budget.

Republicans say the willingness of the White House to talk about entitlement changes could reinforce the Republican claim that steps need to be taken to preserve Medicare, limiting the ability of Democrats to attack and making the debate mainly about what the steps should be.

Democrats are looking to the budget vote to reshape the election landscape much as President George W. Bush’s proposal to overhaul Social Security did in 2006, particularly among older voters and independents who deserted Democrats in 2010.

A fund-raising e-mail sent Monday by the Democratic Congressional Campaign Committee warned recipients that the Ryan budget would “end Medicare as we know it and force seniors to clip coupons if they need to see a doctor.” It added, “Meanwhile, the wealthy would receive another tax cut.”

Republicans say Democrats are exaggerating the impact of any vote. They say their party has a credible response that the budget preserves Medicare for future retirees since it could collapse under runaway costs if left unchanged. Americans now 55 or older would still be covered under the existing program.