WASHINGTON — As President Obama nears a decision on taking broad executive action to reshape the nation’s immigration system, Republicans are threatening to force a confrontation over what they describe as a power grab by refusing to finance some or all of the moves.

Senator Marco Rubio, Republican of Florida, has said his party could seek to prevent Mr. Obama from taking unilateral action on immigration by removing the funding for it in the annual budget, which will be the top order of business when Congress returns from its break and must be passed by the end of September.

Injecting the immigration issue into the annual budget discussions raises the possibility of a spending stalemate that could lead to another government shutdown in the fall. Such a confrontation would pose a risk for both parties: Republicans were largely blamed for the shutdown last year, and many Democrats are wary of an immigration vote just before they face voters in November.

“There will have to be some sort of a budget vote or a continuing resolution vote, so I assume there will be some sort of a vote on this,” Mr. Rubio said Tuesday in an interview with Breitbart, a conservative website. “I’m interested to see what kinds of ideas my colleagues have about using funding mechanisms to address this issue.”