(Adds details on vote, budget goals)
By David Lawder
WASHINGTON, May 5 (Reuters) - The U.S. Senate on Tuesday narrowly passed a Republican budget plan that prescribes deep domestic spending cuts to eliminate deficits by 2024 and aids the party's goal of trying to dismantle President Barack Obama's signature healthcare law.
The first combined House-Senate budget in six years passed 51-48 with all Senate Democrats and two Republicans voting against it, presidential candidates Ted Cruz and Rand Paul.
Senator David Vitter, a Republican who is running for Louisiana governor this year, did not cast a vote.
The non-binding resolution does not go to Obama's desk to be signed into law. Instead, it helps guide Congress' consideration of government agency spending bills and serves as a Republican fiscal policy manifesto that will influence 2016 election campaigns.
The blueprint would slash spending on the social safety net, education, infrastructure and other domestic programs by $5.3 trillion over 10 years with no tax increases. At the same time, it boosts defense spending next year by adding about $38 billion to an off-budget war operations account.
Senate Republicans hailed it as the first balanced budget plan since a 2001 surplus, hoping to score points among voters worried about mounting U.S. debt levels.
"American families know they can't live on borrowed money, and neither can the federal government," said Senate Budget Committee Chairman Mike Enzi. "This balanced budget shows these families that if they can do it, so can we."
But most of the prescribed cuts will be ignored, as the new budget plan does not instruct congressional committees to implement them. Instead, the "reconciliation" instructions are focused on easing the way to repealing the Affordable Care Act.
These provisions will allow Republicans to use procedural tools to pass such legislation with only a simple majority in the Senate, rather than a near-impossible 60-vote threshold that would otherwise be needed.
While Obama is certain to veto any Republican bill to repeal his biggest domestic policy achievement, he may be more willing to compromise on changes to "Obamacare" if the U.S. Supreme Court in June strikes down the law's health insurance subsidy mechanism in many states.
In debate on Tuesday, Democrats played up the hardships that would result from the budget's deep cuts to food stamps and healthcare for the poor, as well as college tuition grants.
"That's what they want to run on? Be my guest," said Democratic Senator Richard Durbin, referring to the 24 Republican senators seeking re-election in 2016 (Reporting by David Lawder; Editing by Eric Beech and Lisa Lambert)