Bill Clinton did not wrap the 1992 nomination up in June. May? Nope. April? Try again? Here's an article from the NY Times, dated MARCH 20, 1992. MARCH 20, 1992.
"Former Senator Paul E. Tsongas of Massachusetts withdrew from the race for the Democratic Presidential nomination today, a decision that many in his party said all but insured the selection of Gov. Bill Clinton of Arkansas.
Mr. Tsongas announced his departure at a news conference in Boston, where he said his campaign did not have enough money to continue. His move leaves only former Gov. Edmund G. Brown Jr. of California to compete with Mr. Clinton in the remaining primaries and caucuses in 21 states."