One senior Republican official with knowledge of her plans said that the Jan. 6 riot soured her desire to seek office, but that she would decide over the next few months whether to run as part of a coordinated Trump family comeback.

If negotiating a post-Donald-Trump world has been a disorienting experience for Republicans around the country, it is especially acute in North Carolina, a state that has become a polarized, and nearly deadlocked, partisan battleground.

Mr. Burr’s vote, and the torrent of criticism among North Carolina Republicans that came with it, appeared likely to sharpen the differences in the primary to succeed him between staunch Trump loyalists and Republicans who see a need to appeal to educated suburban voters in a state with steadily changing demographics.

“The G.O.P. base is getting smaller,” said Paul Shumaker, a veteran party strategist in Raleigh.