No, actually there was among Northeastern Republicans like Roosevelt and Lodge, as well as prominent businessmen. FWIW, America was strongly anti-war as late as 1917. But once it was clear that Germany had violated America's neutrality Wilson pushed for a declaration of war - and he got it by a wide margin in Congress. There's no reason that TR wouldn't be able to do the same in 1915. He necessarily get a war declaration immediately after the Lusitania - but he probably would be able to in the next month or so once the Transatlantic situation escalates from there.
Wilson got a declaration of war because Germany had launched all-out USW against
all ships - American ones included. In 1915 they backed off from that eve in the face of Wilson, and would do so even quicker in the face of TR - if indeed the
Lusitania gets sunk at all with TR in the White House.
I'm not sure what you mean about the transatlantic situation "escalating". Whatever that means, it certainly didn't involve wholesale attacks on US shipping - the
only thing that would have made war a serious possibility. Absent that, America stays neutral - totally
regardless of who is President. Till that happens, TR's wishes are totally irrelevant.
If, for some reason, you want America in the war sooner, you need a change of policy in
Berlin. Nothing that happens in Washington is going to bring it about.