US loses the SAW, one of two things happens in 1900, Roosevelt gains control of the GOP on a hawkish pro-military platform and wins the election against Bryant who IOTL spent the war with malaria in FL, or McKinley loses badly to Bryant.
Roosevelt gaining control of the Republican's would largely depend on what he does in Cuba, if he's seen as a hero in an otherwise f-up campaign, than he would be a no brainer. He can paint himself as someone who had the foresight to push to upgrade the US Navy which he did at his time in the Department of the Navy, which he basically ran.
Bryant can be painted as the "Cowardly Lion" that he was IOTL or, depending on how long the war goes, could be painted the same way that Roosevelt is in the above paragraph, minus the Navy work. He could also win on an isolationist, anti-imperial campaign.
Of course, if TR gets shot dead then he won't be doing much afterwards! Even if not dead, he might spend the balance of the war as a prisoner or in hospital - neither is dishonourable or a barrier to success, except that it removes him from the public conscious in the immediate aftermath of the war
Best Regards
Grey Wolf