"difficult burden" is a correct and usable phrase in written English.
It is typically used to describe a challenging or heavy responsibility or problem that someone must carry or manage. Example: The loss of his job placed a difficult burden on John, as he struggled to support his family and pay his bills.
"It's a very difficult burden".
That was a difficult burden, since Mr. Espada's co-defendants were the co-signatories for the health plan.
"That's a very, very difficult burden: to start in your first year," Paul Hackett, the Jets' offensive coordinator, said recently.
The White House has yet to meet the difficult burden of showing why Iraq's weapons programs, including its efforts to develop nuclear arms, require an American invasion.
"But the possibility that a young man could spend a significant amount of time in prison poses a difficult burden on me, considering my rudimentary knowledge of criminal procedure".
This is bizarre, given that Bullock is one of the few leading ladies — Meg Ryan having temporarily vanished into the mists — who know how to carry a comedy, and to make that difficult burden seem as light as a kite.
"It offloads from the teacher one of the most difficult burdens she has".
"While we strongly believe this was the right and ethical course of action, this did place additional, difficult burdens upon the newly merged organization at a critical juncture," Ms. Nunn wrote.
Without this sort of swap, it would be difficult to burden "the German taxpayer with the new Greek package and its significant risks".
After winning the primary by appealing to the party's base with a strong conservative message, Mr. Schundler faced a difficult new burden: showing that he was not too conservative for a broader electorate dominated by moderates.
Given the high total cost of treatment and the pending loss of international funding, ART will soon become an unbearably difficult financial burden for both the government and patients, necessitating the discussion of a copayment scheme for ART.
