“I am definitely planning to pursue the Constitutional option on the first legislative day,” said Senator Tom Udall of New Mexico, one of several Democrats elected in 2006 and 2008 who have spent months mapping how to overhaul the Senate process. “What will happen as the result of that will depend on the 99 other senators.”

Mr. Udall and others say they do not intend to seek any change that would overturn the Senate’s fundamental requirement that it takes 60 votes to cut off debate and force a final vote on a disputed bill or nomination.

But they say they want, at a minimum, to speed up debate over the initial attempt to bring a measure to the floor and to force senators to be on the floor debating if they are blocking a measure, much like Jimmy Stewart did in the movie “Mr. Smith Goes to Washington.” By contrast, the modern version of the filibuster allows seemingly endless breaks in floor activity with rows of empty desks as a backdrop.

“If you have a passion for something and you want to stand up and rouse the country, then you have to do it,” Mr. Udall said.

Another change under consideration would end the practice of secret “holds,” which allows a single senator to block any piece of legislation or nominee. This change has drawn bipartisan support in recent months.