Trump has said he would consider keeping parts of the landmark health care plan, but repealing Obamacare does not imply doing away with parts of the plan that are popular: allowing children to remain on their parents’ health care insurance until the age of 26 and preventing health care insurers from denying coverage because of preexisting conditions. Nor does repealing Obamacare imply doing away with the expansion of Medicaid and the creation of insurance exchanges where individuals who don’t receive insurance through their employer can purchase insurance. Millions of people have been added to the rolls of the insured, and the repeal of Obamacare should not deprive the newly insured of this benefit.

Nevertheless, the policy changes needed to save the existing system from a death spiral are fundamental, and Republicans should not allow those changes to be characterized as reforming Obamacare. Premiums are skyrocketing, affordable plans have such high deductibles that the insured can still confront crippling health care costs, and the young and healthier cohort—whose enrollment would have helped to lower the cost—have not found it in their self-interest to participate. President Obama has not bequeathed to us a viable health care system, and he should not be allowed to claim Obamacare as part of his legacy.

Names determine who gets credit for legislation. The apolitical may lament the emphasis on taking credit that is a pervasive characteristic of our political class, and long for representatives who selflessly serve the public good; but realists who want to accomplish change work within the parameters of the system. President Obama’s hyper-partisan approach to health care reform is responsible for its failures. Republicans not only have to replace Obamacare with a more viable policy, but they have to make sure that the architects of the new plan get the credit they deserve. If Trump plays a leading role, then why not “Trumpcare”?

There was a time when a more bipartisan approach might have allowed both parties to share credit for health care reform. When President Obama took office, there was a consensus that reform of the health care system was needed. Maine’s two moderate Republican senators, Olympia Snow and Susan Collins, had expressed interest in health care reform. Former Democratic U.S. Sen. Max Baucus, chair of the Senate Finance Committee, had convened the “Gang of Six,” a small bipartisan caucus to hammer out a bipartisan proposal. In addition to Senator Snow, Republican senators Mike Enzi and Chuck Grassley had joined Democrats Jeff Bingaman and Kent Conrad to work together.

Still, given the partisan polarization of the contemporary political system, presidential leadership is indispensable in promoting bipartisan solutions. One of the most powerful techniques presidents have for enticing partisan opponents to compromise and join with the administration is credit-sharing, assuring Republicans that their party will reap political rewards with the electorate for its pragmatic willingness to put the interests of the nation above the interest of party. This was the kind of leadership Lyndon Johnson showed in passing the 1964 Civil Rights Act, generously giving credit to Everett Dirksen and the Republican Party for supporting the measure against die-hard southern Democratic opponents of the measure.

The president could have chosen to rise above his party and propose reforms that would have been endorsed by at least some Republicans. But Obama abandoned such an approach for health care reform when his steadfast support was most needed. Bipartisanship would have required Obama to sacrifice his aspirations to be a transformational president along the lines of Franklin D. Roosevelt (a bipartisan proposal would have been more incremental than transformational), and he would have had to bypass a congressional leadership structure that was indelibly infected with hyper-partisan animosity.

Instead, Obama relinquished control over his health care plan to then U.S. Speaker of the House Nancy Pelosi and then U.S. Senate Majority Leader Harry Reid, two of the most partisan figures in Washington. Believing that Hillary Clinton had failed in her health care reform efforts in 1993 because she centralized control over the process in the executive branch and failed to involve Congress, Obama overcorrected and placed too much reliance on partisan congressional leaders to work out the details of the legislation. As Obama stepped back, bipartisan efforts faltered. Given firm Democratic control of the House and a filibuster-proof majority in the Senate, Democrats knew that they could enact the Affordable Care Act without any Republican support as long as Democrats remained unified. The death of Senator Ted Kennedy and the upset electoral victory of Republican Scott Brown to replace him forced the Democrats to short-circuit normal procedures to achieve their end game, but Obamacare was enacted in March of 2010 without a single Republican vote.

Democrats will never accept fundamental changes in the program and they will never relinquish the partisan advantage that goes along with their claim to have created an entitlement to health care. The time for bipartisanship in health care has passed. Republicans must replace Obamacare with Trumpcare (it has to have a new name no matter how many elements of Obamacare are preserved), and they will probably have to exercise the nuclear option and eliminate the filibuster to accomplish this goal. Even in a two-party system, one party is typically dominant. This is not a time for Republicans to “go wobbly.”

Donald Brand is a professor of political science at the College of the Holy Cross.