(CNN) There is nothing unusual about a new president arriving in Washington with a promise to right the perceived wrongs of his predecessors. George W. Bush pledged ''to restore honor and dignity'' to the White House after the Clinton scandals and Barack Obama took the reins with a notion of mending a nation divided by war and increasingly dislocated by a spiraling economy.

In that way, President Donald Trump is very much like those who came before him. His candidacy was staked on a twin rejection of Washington's "swamp" culture and, in more specific terms, Obama's political and cultural legacy. The decision to withdraw the US from the Paris climate deal has elements of both -- the potential to undermine of one of Obama's defining accomplishments while at the same time issuing a broader rebuke to a global order the former president valued and sought to empower.

Still, Trump has registered only mixed results as his campaign promises, and the promise of dismantling Obama's accomplishments, come up repeatedly against the stricter realities of governing.

Trump's victories

Trump has succeeded in undermining a host of other Obama administration priorities. Environmental action, with regard to the Paris pact, but also in the more mundane and familiar regulatory theater, has been either limited or reversed. A pair of contentious pipeline projects -- Dakota Access and Keystone XL -- have been advanced by the new administration in defiance of Obama White House decisions to slow or stop them.

But it has been in the criminal justice arena where the Trump agenda -- with Attorney General Jeff Sessions leading the way -- is running up against the Obama legacy, and repeatedly turning it back. The Justice Department under Sessions has in only a few months taken aim at some of the previous regime's highest profile decisions.

"This is a new era," Sessions told border patrol agents in Arizona last month. "This is the Trump era."

What does that mean, exactly? On the border, per Sessions' remarks, it portends stepped up efforts to prosecute undocumented immigrants (see above) and more resources -- immigration judges, for instance -- to ensure the quick removal of those convicted.

The same goes for voting rights and, in particular, the fight over voter ID laws. Sessions in February asked a federal court to dismiss a claim joined by his predecessors seeking to strike down a Texas law they alleged had been crafted to suppress minority turnout. (A judge in April sided with the challengers , ruling that the legislation "had a discriminatory impact.")

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The stickier points

A little more than four months into his term, the new president has moved quickly to reverse or eliminate Obama era legislation, executive actions and international agreements. The most contentious fight has centered on health care and the long Republican effort to repeal Obamacare. But even with majorities in both chambers of Congress, the White House and GOP leadership have struggled to craft a politically feasible replacement.

The bill passed out of the House, revised in relative secret and voted on without a proper accounting of its likely effects, is expected to languish in the Senate, where Republicans in that chamber are only beginning to craft their own version. A new poll from the Kaiser Family Foundation found that only 8% of respondents wanted to see the House bill proceed to Trump without significant edits. With an assortments of hurdles still to clear, Obama's signature legislative achievement looks safe -- at least for now. The same goes for some of his more popular executive actions.

The use of torture, which Obama effectively halted but Trump rallied to reinstate while on the stump in 2016, seems unlikely to make a return, if only because the moderate military veterans with key places in the administration have advised against it. More notably, Trump's core campaign message -- a crackdown on illegal immigration and undocumented immigrants -- has also hit roadblocks.

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His border wall, which was to be built with the Mexican's government's money and acquiescence, seems stuck in the mud. As it relates to Obama, the pace of deportations under Trump had actually decreased, as of late April , according to statistics provided to CNN from Immigrations and Customs Enforcement (ICE). But arrests of undocumented immigrants have gone up, in particular of the non-criminal variety. Trump has publicly assured that DACA protections, offered to undocumented immigrants who arrived as children with their parents, would remain in place. But there have been conflicting reports on actual enforcement tactics and the issue is now headed for the courts

The forecast

While Trump's agenda has been thwarted at a number of notably contentious passes, the travel ban foremost among them , his broader effort to dismantle the Obama legacy have found success, ironically, through the most traditional means. Sessions and the Justice Department enjoy wide discretion and have exercised it, much like environmental legislation and regulation have taken hits authored by appointees and Republicans in Congress.

Whether the White House is willing to further defer or offload the grittier work to those establishment figures, especially in light of congressional stumbling on health care, could go a long way in determining the fate of Obama's most prized feats.