It depends on when in the 80s that they're elected. If Ford wins in 76, a Democrat is going to win BIG in 1980, and because a moderate like Carter lost them a winnable election in '76, we're going to get a liberal democrat to succeed Ford. If this is the case, you get New Deal, Great Society, New Frontier, or Fair Deal 2.0, and unless they appoint someone like Volcker early in their term, they're going to struggle with the economy and struggle to get re elected.
If Carter beats Reagan in 1980, his second term goes more or less the way Reagan's first did, although I see Carter handling the AIDS epidemic better than Reagan did. The economy probably double dips like it did OTL, the 82 midterms go to the GOP with them taking the Senate and possibly the house. Carter probably handles Lebanon better than Reagan to. As for 1984 TTL, the economy will be recovered by election day. Assuming a two term Vice President Mondale is the Democratic nominee, it all depends on how he does. If he runs similar to OTL, the GOP wins, if not, he wins. Expect a Republican as early as 88, but no later than '92.
If some Democrat somehow beats Reagan in 1984 (I can only picture a moderate doing this), picture Bill Clinton's Presidency in the 1980s (and early 1990s if said Democrat is re elected in 1988) and that's what you'll get.
In either case, there is no SDI, a safer 1983, a Cold War that possibly ends earlier than OTL, but no latter than OTL, and no weapons sale to Iran. Also expect homelessness to be less of a problem. As you can tell, I'm no fan of Reagan.