WASHINGTON — Making good on last fall’s campaign commitments, Republicans advanced conservative budgets in both houses of Congress on Wednesday, setting up a veto struggle over the fate of the health care law and promising a whopping $5 trillion in spending cuts to erase deficits by the end of the coming decade.

The possibility of billions more for the Pentagon and an overhaul of the tax code also emerged as Republican priorities, although there were significant differences between the day-old proposal in the House and the one unveiled Wednesday by Senate Republicans.

Defense spending aside, Medicare was chief among them. Senate Republicans, already eyeing the 2016 elections, balked at a politically sensitive House plan to turn health care coverage for seniors into a voucher-like program for those who enroll beginning in 2024.

Republicans claimed a balanced-budget, no-tax-increase approach. Senate Majority Leader Mitch McConnell of Kentucky said President Obama’s budget from earlier in the year raised “taxes by nearly $2 trillion, and increased the national debt by more than $7 trillion. In other words, it was more of the same old tired, failed policies of the past.”

He said the Republicans promise a plan “that will support economic growth and more opportunity for hardworking families, while protecting our most vulnerable citizens.”

It will be weeks or months – if then – before Republicans can turn their nonbinding blueprints into legislation and send it to the White House for Obama’s signature or veto.

Before that, they will concentrate on pushing the rival budgets through the two houses. Next, they will try to agree on a compromise that they concede will stand as a test of their ability to govern.

Republicans promised during last fall’s campaign that they would try to balance the budget if they won control of Congress. They also said repeatedly that they would work to eradicate the health care law that Obama has pledged to defend, and has provided coverage to more than 16 million individuals who previously lacked it.

Details contained inside the budgets make a veto struggle with Obama over the health care law a virtual certainty. Senate Republicans said they intend to use legislation that Democrats cannot block to accomplish that goal.