Democrats in Congress have been relentless about casting the government shutdown clash as a fight over helping Americans pay for health insurance.

But there is another, far deeper issue driving the impasse: their outrage about what is happening across the country under a president they regard as lawless and unchecked.

While Democrats believe they have a winning political argument in demanding the extension of Obamacare subsidies, they are also motivated by Mr. Trump’s extreme policies and tactics, and his penchant for running roughshod over the legislative branch with scant pushback from congressional Republicans. That is one reason that the shutdown impasse has dragged on, with no immediate move toward resolution and little sign that Democrats’ resolve is flagging.

Democrats have watched with increasing alarm as the administration has ignored congressional spending directives, dispatched the military to American cities, ordered government retribution against Mr. Trump’s perceived adversaries and mounted an aggressive immigration roundup that has prompted fierce fights in the courts.

Empowering the Trump administration and its perceived abuses by funding the government is an extremely hard pill for Democrats to swallow.

“The issue that we are debating,” Senator Bernie Sanders, the Vermont independent, said on the Senate floor on Tuesday, “is not just health care, as enormously important as that is. What we are talking about is whether we are going to allow our country to move toward an authoritarian society, run by a president who is a megalomaniac, who wants more and more power in his hands, who does not respect the rule of law or the Constitution of the United States of America.’’

Democrats have good reasons to center the shutdown fight around the extension of pandemic-era Obamacare health insurance subsidies. They fear that millions of Americans could see their coverage costs soar or become unaffordable without quick action by Congress. It is a unifying subject and has strong political resonance. The impact of not intervening would be felt by both Democratic and Republican voters, providing an opening to reach across the aisle for a solution.

“The health care fight is the right fight for us to be in,” said Senator Peter Welch, Democrat of Vermont. “And one of the reasons I think the health care fight is the right fight is that the folks who are going to be hurt are folks who voted for Trump, and folks who didn’t.”

But a key reason that Democrats have held firm since the shutdown took hold — a stance that runs counter to their usual political instincts and interests in favor of government services — is their conviction that the president is abusing his power and cannot be trusted to abide by any conventional political deal.

Democrats employ language in describing the Trump administration that would be considered extraordinary in the past, but is becoming almost commonplace now, illustrating the depth of their apprehension about the administration and their dark view of its capabilities.

Senator Patty Murray of Washington, the top Democrat on the Appropriations Committee and one of the lawmakers central to ending the spending impasse, described the Trump administration this week as “run by crooks and cowards.”

Others were equally disparaging.

“We have a government that has been hijacked at the highest levels by people who act like mob bosses,” Senator Andy Kim, a New Jersey Democrat who was elected just last year, said in a floor speech. “I’m from Jersey. We know a thing or two about mob bosses.”

Senator Richard J. Durbin, the No. 2 Democrat and one of those who broke with the majority of his party last March by voting to fund the government, has this time seen Mr. Trump dispatch Texas National Guard troops to his home state over objections from Illinois leaders, a move unlikely to win Mr. Durbin’s support on spending.

“Instead of working to find a bipartisan way to reopen the government and lower the cost of health care, President Trump is solely focused on scoring points against his perceived enemies,” Mr. Durbin said.

Simmering in the background of the standoff is deep Democratic resentment over how cavalierly Mr. Trump and his budget director, Russell T. Vought, have trampled on congressional spending authority by freezing funds, eliminating spending on bipartisan programs and pushing through spending cut packages with Republican acquiescence.

Threats by Mr. Trump to fire thousands of federal workers during the shutdown have only hardened the Democratic position.

A secondary goal of the Democrats in the standoff is to win guarantees against the administration overriding congressionally approved spending plans in the future, though Democrats have chosen not to emphasize that aspect. They see it as inside baseball and do not want to distract from their focus on health insurance, which has more relevance to the general public.

Democrats also worry about the willingness of their Republican congressional colleagues to enforce any agreement, even though they say their G.O.P. colleagues assure them privately that they intend to resist more attempts by the White House to counter spending approved by Congress.

But so far, congressional Republicans have stood by complacently as Mr. Trump has usurped congressional authority in numerous ways, including his widespread imposition of tariffs without congressional action, and his instigation of military actions, such as deadly attacks on boats that the administration said were ferrying drugs in the Caribbean Sea. A Democratic attempt to block those strikes won just two Republican supporters Wednesday night as the measure failed in the Senate.

Senate Republicans have also found ways to sidestep Democrats this year by stretching the rules covering what legislation is subject to the filibuster, and changing the rules to overcome Democratic opposition to Trump nominees. Now Republicans are demanding Democratic votes to fund the government and blaming their colleagues for the mounting damage in the shutdown.

“They just can’t fathom having to deal with us,” said Senator Brian Schatz, Democrat of Hawaii. “They haven’t needed our votes. And so this is the first time that they’re confronted with the idea that we are not irrelevant, and it is making them angry.”

Republicans attribute the Democratic refusal to reopen the government without concessions on health insurance to their desire to placate elements of the party that have insisted on blanket resistance to Mr. Trump at any cost.

“It is sort of this blind Trump derangement syndrome if you will,” Senator John Thune, Republican of South Dakota and the majority leader, said on Fox News. “They don’t want to give the president a victory on anything.”

Democrats say their apprehension about the Trump administration is well-founded, given what they have witnessed and experienced so far. But they say a spending agreement is possible despite their ominous view of the Trump administration.

“We’ve got to have faith we can get through this,” said Mr. Welch. “We’ve got to maintain as much as we can.”