It is premature, if not naive, to say that the new Congress, which started Tuesday, heralds a new era of bipartisanship. Better for U.S. Republicans, with a firmer hold on the House and an eight-seat majority in the U.S. Senate, to focus on a more modest goal: being less scary.

That’s not meant as an insult — the advice comes from no less than Senate Majority Leader Mitch McConnell, who says his party’s job is to show voters that if they elect a Republican president in 2016, it wouldn’t be “a scary outcome. I want the American people to be comfortable with the fact that the Republican House and Senate is a responsible, right-of-center, governing majority,” he says.

Republicans might adopt a few basic criteria for fulfilling the promise of those three adjectives. They could begin by presenting legislation that is both ideologically mainstream and broadly backed by members of their own party.

A bill to expedite the Keystone XL pipeline to transport oil from Canada to Louisiana, for example, is an ideal starter. Republicans support it, as do many Democrats. And if President Barack Obama were to veto the legislation, the onus would be on him to explain why. Trade deals in the Pacific and elsewhere are significantly more complicated, but the White House is supportive and the necessary legislative coalitions appear within reach.

The harder test of Republican governance will come by the end of next month, when Congress must provide funding for the Department of Homeland Security. In last month’s lame-duck session, Congress slashed the department’s budget as a way to register conservative ire at Obama’s executive actions on immigration.

It’s unclear, to put it mildly, how withholding money for homeland security fits the party’s “responsible” rubric. It’s equally unclear how Republican extremists will stomach a likely capitulation to that reality. In any case, the train of contentious issues — Medicare doctor reimbursements, tougher Iran sanctions, raising the debt ceiling — won’t stop.

To stay on track, Republican leaders will have to devise a congressional version of “triangulation,” the tactic that President Bill Clinton deployed two decades ago to hold the center ground between Republicans and his liberal base. The right wing of the Republican Party is far more powerful and potentially destructive than anything Clinton faced in his ranks. For the Republican leadership, that only makes triangulation more necessary.

To be responsible — and responsive to the vast middle of America — House Speaker John Boehner and McConnell will need to somehow placate or marginalize their party’s most avid and outlandish partisans. If the speaker and majority leader can notch a few smart legislative wins in the next few weeks, perhaps they can use the resulting momentum to hold their party in line _ and offer the model of conservative governance that their members and constituents deserve.

— Bloomberg News