So Bush wasn't strong on defense? Who is an example? I'll let Seamus speak for himself, but if "strong on defense" means insert ground troops at the drop of a hat (of course I'm framing it that way because it sounds bad to me), didn't Obama do that in numerous countries throughout Africa and Asia, with special forces and training missions? If it's budgetary, lavish defense spending is bipartisan. If it's about being willing to start a major ground war, I don't recall any candidate in either party explicitly calling for the real deal, like explicitly a ground invasion of Syria/Iran or direct strikes against Russian armed forces... You'll have to explain yourselves.
I can only speak for myself of course but overall Bush was strong on defense, but only in that he stopped the 90s decline. His allowing it a seemingly endless budget with little to no oversight as well as getting us into Iraq which ended up eroding our ability to fight conventional wars has made us qualitatively weaker in peer to near peer fights.
Best example would probably be Bush Sr. Shrink the military from Cold War to peacetime in order to spend that money elsewhere but not to shrink it so much that we're strapped in the event we need to fight a war ( if we needed to fight desert storm again with similar troop numbers it would take nearly our entire active duty army).
I'm actually a proponent for forcing our military to work with a smaller budget. Surely we can get rid of a lot of the Flag positions, research into silly things like exoskeletons and robotic mules, and so on without having to shrink the military. It would require real oversight into acquisitions so we're not paying a half million dollars per vehicle for the the humvee replacement (the JTLV) or the endless boondoggle known as the F-35. A lavish military is the easy cop-out for appearing strong on defense and a typical American method. If it's got a problem throw money at it till it works.
I would say it would require being willing to start a major ground war. The ability and willingness to do so is what makes a deterrence effective. That willingness needs to however be governed by oversight by Congress, a blank check to start wars that aren't emergencies affecting our national security is unconstitutional to say the least. Congress having abdicated its role in war and foreign policy is what has allowed the Trump era to become so dangerous to our international relations and norms.
I don't want a war with Iran or Russia or anything at the moment. However we need to ensure we've got the ability and the will to defend our allies be they South Korea, Japan, the Philippines, Taiwan, NATO, etc.. Obama's pivot to Asia with no additional forces or or increase in military cooperation was seen as toothless as it actually was. TPP was the only achievement and unfortunately he couldn't get Congress to ratify it. All his training missions in Africa are just soft power and the use of SOF is rather limited outside of what they were doing in Syria and Afghanistan.
As for direct strikes on Russia, that'd be extremely dangerous. George W. Bush knew that we when Georgia stupidly went to war with Russia over South Ossetia. The Russians saw also that we were happy to expand NATO to their borders but that war also showed that we were not willing or able to contest them in their 'near abroad'. How do you stop a Russian invasion of Crimea? You'd probably have to be willing to risk WW3 on the matter as Truman did with the Berlin blockade and Kennedy did with the Cuban missile crisis. Right now we'd be unprepared for that type of war and Russia knows it, correcting that weakness would be a good start for actually being strong on defense. Same goes for China, at some point they will contest our defense of Taiwan and a political unwillingness to actually defend that ally will probably let them be abandoned by us. I fear that if the US is in a 'why fight for Danzig' moment that we will take the easy way out and let our allies down. Trump's vocal questioning of why we should defend Montenegro is a fine example of it.

Funny you should mention that, because progressives have (at least since last year) been crapping endlessly on the DNC/DCCC for prattling about "identity politics" yet consistently intervening in local primaries to support white (often male) military veterans (or business persons) over women and minorities with more populist platforms.
It's part of a good turn around (in my mind) so that the Republicans can stop pretending to have ownership of American patriotism. It what's allowed things like the NFL kneeling controversy go from a free speech issue to a patriotism/respect our veterans thing. Also the more populist platforms play well to Democrats but to win general elections in solid republican states will probably require a more moderate approach. This would go more toward the thread on compromise. Going cold turkey into policies usually doesn't fair well, on many issues it's best to ease into them overtime. I don't mean things like abortion or civil rights but things like universal health care and pensions. Drastic change over a short period usually causes strong reactionary movements (like the Tea Party or Trumpism...).

As for Hillary, without revisiting particulars of her career or person I recall polls showing that her favorability was fairly high among the general population between 2010 and 2015; it's more that she was susceptible to the election propaganda machine, partly because it had a generation to really get in motion, and wasn't effective at counteracting its impact.
Susceptible to propaganda equals politically toxic in my explanation. A generation of her being painted a witch doesn't make here a viable candidate in the solid Republican states that hate her.