For months, Donald J. Trump’s supporters have praised his instant command of the news media microphone. His ability to garner so-called free media is unrivaled.

But as last week demonstrated, not all of it is positive.

As it turns out, the highlight of Mr. Trump’s week were his meetings on Thursday with the House speaker, Paul D. Ryan, and the Senate majority leader, Mitch McConnell of Kentucky. The next day, Mr. Trump was engulfed in stories about a recording of a man who identified himself to a magazine reporter in the early 1990s as “John Miller,” a spokesman for Mr. Trump. But “John Miller” sounded very similar to Mr. Trump, and he acknowledged years ago that he would sometimes employ other names while pretending to be his spokesman.

Mr. Trump forcefully denied that the recording was of him. But news outlets secured audio experts who argued otherwise, and the story dominated the headlines on Friday — alongside questions about Mr. Trump’s statement that he did not believe the public had a right to see his tax returns.

Democrats were slow to seize on the tax returns as an issue, but Hillary Clinton’s advisers say they will seek to highlight the issue.