WASHINGTON — House Democrats sought on Thursday to pre-emptively dismantle President Trump’s core defenses in his impeachment trial, invoking his own words to argue that his pressure campaign on Ukraine was an abuse of power that warranted his removal.

On the second day of arguments in the third presidential impeachment trial in American history, Democrats sought to make the case that Mr. Trump’s actions were an affront to the Constitution. And they worked to disprove his lawyers’ claims that he was acting only in the nation’s interests when he sought to enlist Ukraine to investigate political rivals.

In doing so, they took a calculated risk in talking at length about Mr. Trump’s targets — former Vice President Joseph R. Biden Jr. and his son Hunter Biden — and underscored the political backdrop of a trial that is unfolding only 10 months before the election and is likely to reverberate long after the verdict.

“You know you can’t trust this president to do what’s right for this country — you can trust he will do what’s right for Donald Trump,” said Representative Adam B. Schiff, the lead impeachment manager, said in an impassioned appeal as the clock ticked past 10 p.m. “This is why if you find him guilty, you must find that he should be removed. Because right matters. Right matters and the truth matters. Otherwise we are lost.”