YOUNGSTOWN, Ohio — Republicans Marco Rubio and John Kasich are fighting for their political futures Tuesday, desperate for wins in their home states of Florida and Ohio to keep their White House hopes alive and complicate Donald Trump’s path to the nomination. Democratic front-runner Hillary Clinton is hoping to keep rival Bernie Sanders from building new momentum in the Midwest.

With more delegates up for grabs than almost any other day in the primary calendar, Tuesday’s contests afford Trump and Clinton the chance to put their parties’ nominations out of sight for their competitors. While Florida and Ohio are the biggest prizes, Missouri, Illinois and North Carolina are also awarding a cache of delegates.

Trump enters Tuesday’s primaries embroiled in one of the biggest controversies of his contentious campaign. The GOP front-runner has encouraged supporters to physically confront protesters at his events and is now facing criticism for encouraging violence after skirmishes broke out at a rally last week in Chicago.

During an event Monday in Tampa, Trump was interrupted intermittently by protesters, some of whom were forcibly removed. Trump said he didn’t want to “ruin somebody’s life, but do we prosecute somebody like that?”

The vibe at Trump’s events has deepened the angst over his candidacy in some Republican circles. Rubio and Kasich have suggested they might not be able to support Trump if he’s the nominee, an extraordinary stance for intraparty rivals. House Speaker Paul Ryan has also taken lightly veiled shots at the businessman, who has denied playing any role in encouraging violence against protesters.