The initiation of a formal impeachment inquiry carries grave political risks for Democrats, allowing Mr. Trump and congressional Republicans to argue that Democrats are unfairly tormenting the president for partisan gain with an election just more than a year away. “PRESIDENTIAL HARASSMENT!” Mr. Trump tweeted from New York, where he was attending meetings at the United Nations, as Democrats announced that they were opening a formal impeachment inquiry.

Among the main questions for Democrats is how unified they are now on an issue that has created deep rifts within their ranks until this week. It is far from clear, for instance, whether they agree on how broad the impeachment inquiry should be, or who should run it. Already on Tuesday, some more moderate lawmakers from Republican-leaning districts, who put themselves at political risk to embrace impeachment, were privately voicing frustration at the lack of certainty about what the inquiry would look like going forward.

Republicans paid a steep political price in the midterm elections for moving to impeach Bill Clinton in 1998, and some analysts believe this episode could backfire on Democrats as well.

But with the party clamor growing for action against the president after the Ukrainian revelations, Ms. Pelosi and others who had been holding back faced the prospect that failing to move forward on demands to hold the president accountable could cost them more with their own party than pursuing impeachment might hurt them with Republicans and independents. Long a progressive hero, Ms. Pelosi had already drawn fire from the left for failing to act.

Even as momentum rapidly built, worries surfaced among Democrats that the drive could fizzle with the release of a transcript of the telephone call between Mr. Trump and the Ukrainian president if it proved less explosive than anticipated — an outcome Republicans predicted. But the speaker and others said that such an outcome would not deter them and that they wanted to hear all of the whistle-blower’s account of what led to the complaint against Mr. Trump, which is believed to include more than the call.

The decision to back the inquiry was not easy for Democrats who had been hesitant to get on board.

“I certainly didn’t run for Congress to be part of an impeachment inquiry,” said Representative Haley Stevens, Democrat of Michigan, who called the phone call an abuse of power. “It’s heartbreaking to look something like impeachment in the face,” she added. “No matter who the president is, we want them to succeed. At the same time, I have to maintain the rule of law and checks and balances.”

While the revelation of the whistle-blower complaint broke the logjam on impeachment, Democrats were becoming increasingly incensed at the proud defiance of the House by the president and his allies, essentially thumbing their noses at a coequal branch of government empowered to oversee the conduct of the administration. The Trump strategy had been effective as recently as a few days ago, when Democrats seemed stymied in their pursuit of the president with the prospect of a formal impeachment inquiry flagging.