WASHINGTON — In a secured room in the basement of the Capitol in July, Jared Kushner, President Trump’s son-in-law and senior adviser, fielded question after question from members of the House Intelligence Committee. Though the allotted time for the grilling had expired, he offered to stick around as long as they wanted.

But Representative Trey Gowdy, who spent nearly three years investigating Hillary Clinton’s culpability in the deadly 2012 attack in Benghazi, Libya, was growing frustrated after two hours. You are in an unwinnable situation, Mr. Gowdy, a South Carolina Republican, counseled Mr. Kushner. If you leave now, Democrats will say you did not answer all the questions. If you stay, they will keep you here all week.

The exchange, described by three people with knowledge of it, typified the political morass that is crippling the House Intelligence Committee’s investigation into Russian meddling in the 2016 election — and whether the Trump campaign colluded in any way.

But the problems extend beyond that panel. All three committees looking into Russian interference — one in the House, two in the Senate — have run into problems, from insufficient staffing to fights over when the committees should wrap up their investigations. The Senate Judiciary Committee’s inquiry has barely started, delayed in part by negotiations over the scope of the investigation. Leaders of the Senate Intelligence Committee, while maintaining bipartisan comity, have sought to tamp down expectations about what they might find.