All presidential election vote shares between 45% and 48%

Thomas Dewey, 1948: 45.07%
James Buchanan, 1856: 45.28%
William Jennings Bryan, 1900: 45.52%
Michael Dukakis, 1988: 45.646%
John McCain, 2008: 45.653%
Thomas Dewey, 1944: 45.89%
Grover Cleveland, 1892: 46.02%
Donald Trump, 2016: 46.09%
Charles Evans Hughes, 1916: 46.12%
William Jennings Bryan, 1896: 46.70%
Martin van Buren, 1840: 46.81%
Donald Trump, 2020: 46.86%
Mitt Romney, 2012: 47.20%
Zachary Taylor, 1848: 47.28%
Horatio Seymour, 1868: 47.34%
Benjamin Harrison, 1888: 47.80%
George W. Bush, 2000: 47.87%
Rutherford Hayes, 1876: 47.92%

45%-48% is the range in which close-election losers (and some close-election winners--albeit ones who lost the popular vote), and some decisive losers, coexist. If one is getting above 48% of the vote, one is assured of keeping the margin between oneself and the winner under 4%. Amongst elections in which the loser got less than 45%, the only one that was unambiguously close was one in which the winner also got less than 45% (1968). (There are also 1848 and 1892, which some might consider close--but in any case, they would all be outliers; all got a smaller vote share than Horace Greeley in 1872, who lose in a landslide, as well as than Adlai Stevenson in 1952, who lost in what technically would be considered a 'landslide' if the 55% definition is used.)

The highest vote share for a 'decisively' defeated nominee appears to be 47.34%, for Horatio Seymour in 1868 (in an election in which 'other' got less than a hundredth of a percent of the vote). The next-highest would be van Buren in 1840 (when 'other' got 0.31% of the vote), followed by Dewey's 1944 45.89% ('other' got 0.73%), and then McCain, Dukakis, and Bryan in 1900. 

One reason I was curious to do this was Ed Kilgore's comment in 2018, that 

On top of everything else, it’s worth remembering that Trump lost the popular vote in 2016 by more than two percentage points, winning basically the same percentage that big-time loser John McCain won in 2008.

'Basically the same', I suppose--McCain's and Trump's 2016 vote shares both round to 46%, if one rounds to the ones place. (The difference between their vote shares was 0.44%, which would seem to be significant if one is making a > 2% margin out to be as significant as Kilgore seems to be doing.) 

In any case, Trump got his vote share in 2020 fairly clear of any 'big-time losers' in living memory (under Horatio Seymour by almost 0.5%, and above van Buren in 1840 by just 0.05%, but more than 1% above McCain [and nearly 1% above Dewey in '44]). 

In hindsight, Trump would likely have had to have improved his vote share to about 47.5% to win the Electoral College. He lost Pennsylvania, the tipping-point state (for a clean Electoral College win--Wisconsin would have sent the election to the House), by 1.2%, so if he were losing nationally by 1.2% less than he actually did, he would--in theory--have won Pennsylvania, along with the narrower states (Wisconsin, Arizona, and Georgia), securing a 289-EV win, whilst losing the popular vote 50.7%-47.5% (or by 3.2%). States wouldn't actually move like that, of course, but that probably sounds like a fair approximation of the minimum Trump would have had to have done in the national popular vote to win the Electoral College. This would have entailed Trump's getting a higher share than Romney, which sounds like a reasonable prerequisite for a Trump win, but not necessarily his getting a higher share than Bush in '00. (If Wisconsin is counted as the tipping point state, the minimum Trump would have had to have done is get to 47.2% in the popular vote, losing it 51.0-47.2% or by 3.8%.)