WASHINGTON — With control of Congress within reach, Republicans are quietly assembling an aggressive 2015 agenda built around a push for a balanced budget and quick passage of measures, like approval of the Keystone XL pipeline and repeal of a medical equipment tax, to show they can govern.

At the same time, they are warning Republican members who have chafed at their minority status for years that simply holding the majority is no guarantee that they can get all they want. Party leaders say that Republicans will need to be realistic about what they can achieve and that a high level of party unity will be essential since any Senate advantage they gain in the midterm elections is likely to be narrow.

“We need to change our mentality,” said Senator John Cornyn of Texas, the No. 2 Senate Republican. “Because we have been in the minority, some people are used to saying no. We need to find something we can say yes to, something that advances our agenda.”

Fear of a splintered majority was a principal reason top Senate Republicans were determined to fend off Tea Party challenges to incumbents, an effort that culminated last week with primary victories by Senators Lamar Alexander of Tennessee and Pat Roberts of Kansas, two pragmatic Senate veterans considered team players.