WASHINGTON » The Republican majority in Congress is barely a week old. Until just a few days ago, the new sign outside Sen. Mitch McConnell’s office, freshly stenciled with the words "majority leader," was not even screwed in properly.

But an important group of Republicans has already decided that it is ready to move on. Instead of joining party leaders at an annual retreat in Hershey, Pennsylvania, this week, Sens. Rand Paul of Kentucky and Marco Rubio of Florida will be kicking the tires on their presumptive 2016 presidential campaigns.

Paul is making a cross-country swing to meet with supporters from New Hampshire to Arizona. Rubio spent the first part of his week rolling out his new book and will use the latter part to court donors.

A third possible 2016 candidate, Sen. Ted Cruz of Texas, decided not to skip the gathering but still managed to poke party leaders in the eye Monday when he headlined a rival retreat hosted by the Heritage Foundation. In his speech, he accused his party of putting forward a milquetoast policy agenda.

This kind of political free agency, surfacing before the new Senate has passed a single bill, is becoming an early test for the Republican Party as it looks to expand its power and prove its ability to govern in Washington from Capitol Hill to the White House.

The distance between those in the party who are focused on running for president and those who say they have the responsibility to produce a record of accomplishment in Washington also points to a growing divide among conservatives.

In certain corners of the party, there is a measure of apprehension and distrust among conservatives who grumble that their leaders are eschewing ideas that are bold and disruptive for ones that are plain and predictable.

They dismiss as uninspired the policies that Republican leadership has prioritized, like tax reform and trade authority. And they say they are underwhelmed by bills like the Keystone XL pipeline measure the Senate took up this week, which they complain are anodyne and lacking in ambitions.

"That’s a little harsh," Sen. John Cornyn of Texas, the No. 2 Republican, said with a laugh when asked about some of the conservative wing’s criticism of his leadership team’s ideas. "Occasionally there’s some differences about tactics, but I would say we’ve got to look at the whole battlefield and not just the immediate fight in front of us, and so I’m optimistic."

John Feehery, a Republican strategist who was a spokesman to former House Speaker J. Dennis Hastert, said that some of the frustration and pushback from the base is driven by outside groups, eager to rally lawmakers behind goals that may not be achievable with a Senate still far short of a veto-proof majority and President Barack Obama occupying the White House for the next two years.

"You have this aggrieved conservative industry that makes their money by being aggrieved," he said. "Cruz plays well into that crowd because he always wants to lead the party down that primrose path."

On Monday, Cruz sounded almost mocking of Keystone in his speech at the Heritage retreat, saying that Republicans needed to push a broader economic package.

"Jobs are a lot more than Keystone," he said. "We need a jobs agenda, an energy agenda, far broader."

And in an aside that some took as a swipe at McConnell, Cruz said he rejected the argument put forward by some Republicans that the party needs to demonstrate it can govern.

"There are some people in this town who will intone in gravelly voices, ‘We need to get things done,’" Cruz said, lowering his voice. "Oddly enough, the people saying that, it doesn’t really matter what those things are."

Yet both the Republican leadership and the 2016 hopefuls already find themselves enmeshed in a relationship that could be both mutually beneficial or potentially destructive. Sen. John Thune of South Dakota, the chairman of the Republican Conference, said he expected that his party’s presidential candidates "may shoot at us a little bit."

"It’s always popular to bash Washington and kind of create separation," Thune said. "But when push comes to shove, and we’re casting votes on a lot of the issues that are on our agenda, I think you’ll see people recognizing the importance of the team."

What the divergence of ideas between the 2016 hopefuls and party leadership shows, perhaps above all, is that Cruz, Paul and Rubio all realize that their titles as senators could be a liability, and they will need to do whatever they can to distance themselves from the deeply unpopular Congress.

At times it seems as if they cannot be far enough away. In addition to a series of television and radio interviews in New York this week, Rubio scheduled a more elaborate tour for his book, "American Dreams," for the congressional recess in February, which is likely to take him through several early primary states, as well as to places like Texas and Florida, where he will have a chance to court donors. And he may also end up missing votes during a fund-raising swing planned for the last week of January.

Paul was in New Hampshire on Wednesday for events that are aimed at Republican primary voters. He plans to go shooting with supporters at a fishing and game club. There will be a rally with activists who are fighting the Common Core education standards, and a fund-raiser is scheduled in Boston on his way out of town as he spends the rest of the week meeting donors, supporters and business leaders in Las Vegas, Reno, Nevada, and Phoenix.

The would-be contenders are also trying to create separation on issues.

Paul and Rubio have been trying to nudge their party toward considering more unorthodox approaches to fighting poverty and reforming the criminal justice system. But they acknowledge that their ideas will be a tough sell in Congress.

Paul, for example, wants to restore voting rights to felons who were convicted of nonviolent offenses and seal the criminal records of certain juvenile offenders so they will be more appealing to potential employers. Rubio is pushing a plan to replace the earned-income tax credit with what he calls a "wage-enhancement credit" that would allow workers making less than $20,000 to receive a monthly 30 percent government credit, an amount that would gradually diminish as workers approach a yearly income of $40,000.

Conservatives inside and outside Congress are pushing the Republican leadership to put forward more plans like these — even ones that do not stand a chance of passing or help contribute to the image party leaders want of a functioning, governing majority.

Being too focused on governing, some conservatives warn, could set Republicans up for a trap. Rich Lowry, the editor of National Review, said that Democrats would have every reason to block Republicans if Republicans’ focus was on making their party appear functional and capable.

"If your goal is to govern and you think you’re going to be able to govern," he said, "you’re sort of augmenting the veto power that Democrats already have."