Democratic interference in Republican primaries paid off in some places but not others, election-denying candidates were halted in Colorado, and incumbents proved their staying power.
Democrats meddled to boost State Senator Darren Bailey in the G.O.P. primary for Illinois governor. But efforts to elevate far-right candidates in Colorado fizzled.
Illinois, Colorado, Mississippi and Utah are the settings for suspenseful contests at the federal and state level. New York voters will choose candidates for governor and lieutenant governor, and Oklahoma is holding a special primary election for the Senate.
Republican leaders think a moderate nominee for governor could beat Gov. J.B. Pritzker. But the party’s base seems to prefer a far-right state senator — and he is getting help from Mr. Pritzker.