WASHINGTON — The Senate gave final approval Tuesday to the first joint congressional budget plan in six years, ratifying a 10-year blueprint that would cut spending by $5.3 trillion, overhaul programs for the poor, repeal President Obama’s health care law and ostensibly produce a balanced budget in less than a decade.

Along party lines, the Senate passed the nonbinding blueprint 51 to 48, with only two Republicans voting no, Senators Rand Paul of Kentucky and Ted Cruz of Texas. Both are candidates for the Republican presidential nomination who say the budget plan does not go far enough to shrink the government and cut spending.

Despite the broad aspirations of this budget plan, it appeared moribund even before its final passage. For the plan to take effect, Republican committee chairmen would have to draft legislation that would impose the prescribed cuts. But they have made little effort to do so, and committee leaders in both parties are already calling for new negotiations on a more bipartisan approach.

“It’s going to keep us very busy over the next few weeks,” said Senator Lamar Alexander, Republican of Tennessee and chairman of the Health, Education, Labor and Pensions Committee. “We’ll see what comes of it.” His committee is now supposed to draft legislation to repeal the health care law, turn Medicaid into block grants to the states and begin converting Medicare into a program that offers the elderly assistance to buy private health insurance.