WASHINGTON — Republicans in Congress are renewing their political assault on the new health care law, trying to repeal President Obama’s signature domestic achievement as part of the next battle over the federal budget.

Rep. Paul D. Ryan of Wisconsin, chairman of the House Budget Committee and last year’s Republican vice-presidential nominee, said Sunday that his budget proposal will include repeal of “Obamacare,” as his party calls it. That position puts tea party conservatives at odds with others in the party who want to find common ground with Obama on the nation’s fiscal woes after the U.S. Supreme Court upheld the health care law.

“We say we get rid of Obamacare,” Ryan said on “Fox News Sunday.”

Senate conservatives are to press for a vote this week to delay funding for the law as part of a bill that must pass to keep the government running beyond March 27. The House is expected to follow suit.

House Republicans have launched an ambitious push to bring the federal budget into balance in 10 years, a task made easier by the New Year’s tax increase on wealthier Americans, as well as across-the-board budget cuts that took effect this month, known in Washington as the “sequester.”

Ryan also relies on more than $700 billion in Medicare savings that Obama achieved as part of the health care law – cuts the Republican had criticized during the presidential campaign.

“We apply those savings to Medicare to make Medicare more solvent,” he said.

Key to Ryan’s blueprint, to be unveiled Tuesday, is a return to a proposed Medicare overhaul that would create a voucher-like system for the next generation of seniors – when those who are now 55 or 56 become eligible for the program at 65. Under Ryan’s plan, seniors would be given a set amount to apply toward the purchase of private health insurance or the cost of Medicare.

Critics say that would shift health care costs from the government to seniors because there is no guarantee that the value of the support would be enough to pay for an insurance policy.

By picking apart the new health care law, Ryan is setting up a potential internal struggle within the Republican Party.

Ryan would undo the planned expansion of Medicaid, which under Obama’s plan would provide coverage for more Americans beyond its current reach as the health safety net program for the poor, disabled and low-income seniors in nursing homes. Ryan would turn the program over to the states.

But Republican governors are increasingly coming on board with Obama’s proposed Medicaid expansion, which will be partly covered by federal funds, seeing it as a way to provide health care coverage to the uninsured.

Both parties and the president have said they want to avoid a government shutdown.