WASHINGTON — As he prepares to guide Republicans out of the wilderness of the Senate minority, Senator Mitch McConnell, the incoming majority leader, knows his real problem is not corralling mavericks in his party like Senator Ted Cruz. It is persuading other Senate Republicans conditioned to voting no that it is time to vote yes.

“One of my challenges is to try to convince some of my members that passing an appropriations bill is a good thing, not a bad thing,” Mr. McConnell said during an interview in which he looked ahead to assuming command of the Senate on Jan. 6. Mr. McConnell, who was instrumental in holding Republicans together against President Obama and Democratic initiatives, acknowledges that changing the mind-set of opposition he helped instill in his colleagues will be crucial to advancing legislation that will attract Democratic support and force Mr. Obama into difficult choices over whether to sign measures pushed by his adversaries. And that is why his focus will be lawmakers he thinks he can meld into a governing coalition.

“There are two kinds of people in politics,” Mr. McConnell said after the recent blowup when Mr. Cruz, the fiery Texan, and Senator Mike Lee of Utah, another firebrand, forced the Senate into a year-end session that handed Democrats more time to confirm dozens of presidential nominees on their way out the door. “Those who want to make a point and those who want to make a difference.

“All of us from time to time make a point,” Mr. McConnell said. “But it is time now to make a difference.”