Over the past 14 months there have been at least eight complaints against White House officials for potential violations of the statute, according to a review by the agency charged with enforcing it. That number has put the Trump White House on a pace to far surpass the complaints against the staff of his predecessor.

A handful of high-profile violations and the increased number of complaints suggest that, more than a year after taking office, Mr. Trump — who has openly defied many norms of government ethics and transparency — is surrounded by aides who blur the line between their roles as partisans and public servants, sometimes skirting or disregarding altogether decades-old standards that govern the behavior of senior White House officials.

“This is an overall attitude this White House has about these rules, that they are just not all that important or they do not apply,” said Lawrence M. Noble, the senior director and general counsel of the Campaign Legal Center, the nonpartisan ethics watchdog group that filed the complaints against Ms. Conway. “There are clearly gray areas, but it’s not like occasionally they stumble into the gray areas; this seems to be willful ignoring of the rules.”

The Office of Special Counsel, the federal agency which enforces the Hatch Act, has an email inbox and telephone hotline devoted to fielding complaints, and, according to one official, has heard about more potential violations since Mr. Trump was sworn in than is typical, particularly three years before a general election campaign. Over the eight years of Barack Obama’s presidency, for example, the office received a total of six complaints about conduct by White House officials — a number Mr. Trump’s administration has already surpassed.

Not every complaint has led to a finding of a violation, and Mr. Trump’s aides argue that many are meritless claims by political opponents looking for ways to undercut the president. They also point to the increase in the use of Twitter and other platforms that make it more difficult to maintain a bright line between the official and the political.