Thanks to a flurry of Ukraine activity, House Speaker Nancy Pelosi and her Democratic majority have approved more subpoenas to investigate President Trump than they have written laws.

The subpoena issued Tuesday morning to former Ambassador William Taylor marked the 56th that has been publicly acknowledged and aimed at Mr. Trump and his team. That is 10 more than the 46 House bills that have become law this year.

It’s far from a subpoena record, but it is complicating Mrs. Pelosi’s attempt to portray her troops as focused on their agenda.

Perhaps more worrying to Mrs. Pelosi’s cause is the conclusion of a former senior oversight attorney for the House, who said the spate of subpoenas issued this month as part of Democrats’ impeachment inquiry is illegal.

Samuel Dewey, a lawyer at McDermott Will & Emery who used to lead investigations for the House Financial Services Committee, said the House Permanent Select Committee on Intelligence, led by Rep. Adam B. Schiff of California, is not authorized under the rules to lead an impeachment probe.

“Unless there’s a bunch of stuff that’s not public, which would in itself be extraordinary, there is no way he has jurisdiction to conduct an impeachment inquiry. I think his proceeding is illegal,” Mr. Dewey said.

Mr. Schiff’s impeachment inquiry subpoenas have all centered around Mr. Trump’s attempts to rope Ukraine into investigating a potential political opponent, former Vice President Joseph R. Biden. The Washington Times counts 15 publicly acknowledged subpoenas issued on the Ukraine matter so far, including the one Tuesday to Mr. Taylor.

The House also has approved 22 subpoenas related to special counsel Robert Mueller’s investigation into Russian meddling and Trump campaign behavior in 2016, seven subpoenas dealing with the president’s finances, three concerning White House matters such as security clearances or the activities of Trump aide Kellyanne Conway, five subpoenas over immigration policy, three over Mr. Trump’s now-abandoned attempt to ask about citizenship on the 2020 census, and one subpoena to the State Department over U.S. policy in Afghanistan.

Those are publicly acknowledged subpoenas that have been approved or for which chairmen have given notice. Other subpoenas may have been sent in secret, which would mean the ratio of subpoenas to bills could be even higher.

“This is becoming a do-nothing Congress, and it will ultimately cost them the majority in 2020,” said Corey Lewandowski, a confidant of Mr. Trump and the target of one of the 56 subpoenas, sent in August.

Mr. Lewandowski questioned the way Democrats went about calling him. He said it seemed more about confrontation than getting information.

His subpoena was issued even though his attorney told the House Judiciary Committee that he was willing to testify voluntarily — as he had already done for two other committees. But Chairman Jerrold Nadler of New York issued a subpoena anyway. Mr. Lewandowski said he learned about it first from a reporter, hours before his own attorney received notice from the committee.

“Perhaps they wanted to make it a media story,” he said. “I think that the hearing itself was for show.”

He pointed out that the subpoena was issued the same day Mr. Trump was traveling to New Hampshire, where he all but endorsed a potential U.S. Senate bid for Mr. Lewandowski.

He also said the committee treated him differently than Mr. Mueller, who, unlike Mr. Lewandowski, demanded to be subpoenaed.

When during his July hearing a lawmaker asked Mr. Mueller to read parts of his report and he declined, the committee accepted that. When Mr. Lewandowski was asked and tried to decline, he was castigated.

“I just wanted to be treated the same,” he said. “I don’t think they did that.”

Mr. Lewandowski said he doesn’t question the legality of his subpoena. By that point, Mr. Nadler was arguing to the courts that he was engaged in an impeachment inquiry and had received his committee’s approval for 18 subpoenas related to the Russia investigation.

That probe petered out after Mr. Lewandowski’s testimony.

Now the focus is on Ukraine, and Mr. Nadler’s committee has been sidelined.

The Washington Times reached out to staff for Mr. Nadler’s committee and three others responsible for almost all of the subpoenas. None of them responded.

But Rep. Gerald E. Connolly, a Virginia Democrat and senior member of the Oversight and Reform Committee, challenged The Times’ comparison of laws to subpoenas. He said the House can issue the subpoenas on its own but needs cooperation from the Republican-led Senate and Mr. Trump to write legislation.

He said Senate Majority Leader Mitch McConnell, Kentucky Republican, is refusing to pass Democrats’ bills, hurting their legislative record.

“Something becomes law when both parties vote for it. And we’ve passed easily 100 pieces of legislation waiting at the grim reaper’s — Mitch McConnell — desk,” he said. “We’ve got at least 100 more ready to go. They won’t bring it up.”

The House is on a good pace with 46 bills signed into law. Eight years ago, when Democrats controlled the White House and Senate and Republicans led the lower chamber, the House had written 32 bills signed into law at this point.

In 1995, when Republicans took both houses of Congress under a Democratic president, just 23 House bills were signed into law by this point.

Mrs. Pelosi’s tally this year is inflated by nine ceremonial pieces of legislation, such as renaming post offices. Even among the substantive bills, many are tweaks or extensions to current law, leaving few marquee accomplishments.

Mr. Connolly said whatever the ratio, the House is well behind Republicans in terms of subpoena records. When Republicans controlled the House and Barack Obama was in the White House, he said, the Oversight and Government Reform Committee alone fired off “well over 100 subpoenas.”

During the 1990s, when President Clinton was in office, Rep. Dan Burton sent out more than 1,000, including one notorious incident in which he sent a subpoena to the wrong person because he confused two people with similar Asian surnames.

But Rep. Jim Jordan of Ohio, the top Republican on the oversight committee, said the subpoena numbers summed up Mrs. Pelosi’s tenure.

“We’ve been saying this. When the Democrats are completely focused on attacking the president, it’s tough to do what’s best for the country,” he told The Times.

Mr. Dewey, the former House attorney, indicated that Democrats have been more publicly confrontational in their approach to subpoenas than past congresses.

He said his own usual approach was to make a voluntary request to a target for documents or testimony and try to reach accommodations with those who resisted. Only after that failed would a subpoena be necessary, he said. He also said he worked with his counterparts in the other party, notifying them when subpoenas were issued.

“Honestly, if you’re cutting corners on procedure, my experience is you’re hiding something or you’re just lazy,” he said.

Mr. Dewey said Democrats could face a legal challenge over any impeachment-related subpoenas because the House has yet to vote to authorize an inquiry. Mrs. Pelosi created an inquiry by proclamation, turning the reins over to Mr. Schiff. Mr. Nadler, meanwhile, has argued to the courts that he has been in the midst of an inquiry for months.

Mr. Dewey said those arguments aren’t frivolous, but “I think they’re wrong.”

“I do not think as a matter of law that the Judiciary Committee can exercise the impeachment power without a vote of the full House,” he said. “And I think independently of that, I do not think any other committee can exercise the impeachment power.”

He said that could be an argument Mr. Trump’s team could make to defy some of the impeachment inquiry’s demands.

“It’s the defense to a subpoena,” he said. “I think that you would have a way to challenge it.”

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