WASHINGTON — President Obama and Mitt Romney will again debate their visions for the next four years on Tuesday night, and if the campaign so far is any guide, they will not acknowledge that the winner’s agenda could depend on the fiscal showdown between Election Day and Inauguration Day.

If Mr. Romney wins, Republicans say they would seek to delay the year-end deadline for a bipartisan deal by up to a year to give him time to flesh out his budget plans and get Democrats to agree. But even if Democrats and the financial markets go along with the delay, the months before Mr. Romney’s swearing-in could be as crucial to his presidency as the transition period was for Mr. Obama four years ago, when the economic crisis led him to draft a big stimulus package while President George W. Bush still occupied the White House.

Mr. Romney’s ability to foster cooperation at the outset could determine his success on a range of issues. Yet Democrats have been dismissive, at best, about his budget plans, which have few specifics on how Mr. Romney would reduce deficits. He has mostly spoken about cutting taxes and increasing military spending.

Mr. Obama, if he loses, would still be president for the lame-duck Congress, but he would have limited leverage. If he gets another four years in the White House, he already has plans to go right back on the campaign trail to build support for his deficit-reduction framework, Democrats say, and administration officials are debating whether Mr. Obama should make some concession to Republicans to spur negotiations.