WASHINGTON >> The primary victory of a Tea Party-blessed candidate in Indiana illustrates how closely Republican hopes for a majority in the Senate are tied to candidates who pledge to infuse the chamber with the deep-seated conservatism that has been the hallmark of the House since the Republicans gained control in 2010.

Richard E. Mourdock, who last week defeated Sen. Richard G. Lugar, a six-term incumbent, promises to bring an uncompromising ideology to Capitol Hill if he prevails in November. And he is not the only Senate candidate who contends that Senate Republicans are badly in need of new blood.

In Arizona, Missouri, Nebraska and Texas, Republican Senate candidates are vying for the mantle of Tea Party outsider. A number of them say that they would seek to press an agenda that is generally to the right of the minority leader, Sen. Mitch McConnell of Kentucky, and that they would demand a deeper policy role for the Senate’s growing circle of staunch conservatives.

Some say they have not decided whether they would support McConnell, who could find himself contending with the type of fractious rank and file that has vexed the House speaker, John A. Boehner of Ohio.

“We need to shake up the Republicans,” said Sarah Steelman, the Missouri state treasurer, who is seeking her party’s nomination to run against Sen. Claire McCaskill, a Democrat. Asked if that meant new leadership in the Senate, Steelman replied, “Possibly.”

John Brunner, another Missouri candidate, said conservatives needed to have a louder voice in the Senate leadership. “When you bring more people to the team, it raises the bar for everyone,” he said. Referring to McConnell, he added, “There could be people up there who could be sputtering now who could take it up a notch.”

Rep. Todd Akin, a third Missouri Senate hopeful, said, “I haven’t made any commitments to anybody, and they haven’t made very many commitments to me either.”

Deb Fischer, who is seeking the Republican Senate nomination in Nebraska, said, “I don’t think anything is automatic.”

McConnell’s leadership does not appear to be in jeopardy. Aides to McConnell say he has already secured enough votes for his re-election as leader, regardless of the November results. And supporters say such threats have surfaced in the past, only to fizzle after Election Day.

Rand Paul of Kentucky made headlines in 2010 while running for the Senate when he declined to say whether he would back McConnell for leader after McConnell supported another Republican in the primary. Ultimately, McConnell was unanimously re-elected as leader, and his standing has remained solid among Senate Republicans even as he has faced sniping from some on the right who say he is too much of a Washington insider.

McConnell evinced no concern.

“In November, if the American people give us the ability to set the agenda in the Senate, I’m confident our conference will have broad unity around our efforts to repeal Obamacare, reduce the size and scope of government, and prevent job-killing tax hikes,” he said in a statement.

McConnell has already made adjustments. He recently enlisted Sen. Ron Johnson of Wisconsin, a freshman elected with Tea Party backing, to lead efforts to coordinate the Republican messages and agenda in the Senate and the House with the party’s presidential nominee. A spokesman for McConnell, Don Stewart, said McConnell was exploring joining Mourdock on the campaign trail.

But pressure remains. Several Republican freshmen in the Senate — among them Paul, Johnson, Mike Lee of Utah and Marco Rubio of Florida — under the tutelage of the Tea Party kingmaker Jim DeMint of South Carolina, have laid the groundwork for a more conservative path in the Senate, often throwing their own logs on the fire of gridlock that has seized Congress.

The stakes are considerable. The country faces what the Federal Reserve chairman, Ben S. Bernanke, has called a “fiscal cliff” on Jan. 1, when the Bush-era tax cuts of 2001 and 2003 are set to expire and across-the-board spending cuts of more than $1 trillion are to go into effect. If a bipartisan agreement cannot be reached before the end of the year, nearly $8 trillion in deficit reduction could go into force in a sudden rush, a boon to budget hawks but a potential disaster for the fragile economic recovery.

After the election, the losing party is more likely to limp back to a lame-duck session of Congress aggrieved at its perceived mistreatment, and the winners will feel more empowered.

But McConnell’s room to maneuver is shrinking with the rising calls against compromise and the diminishing ranks of Republican deal makers.

In recent months, McConnell has been trying to keep the right flank at bay, voting against a bipartisan highway bill, for example, that conservative members disliked. He has also endorsed an earmark ban, in sharp contrast to former years, when his earmarks for Kentucky were the stuff of campaign fodder.

At times, his attempts to navigate the treacherous divide between placating conservatives and not appearing obstinate fall flat. Late last year, he insisted on a vote on his own alternative to the Senate Democrats’ version of the payroll tax cut bill, to demonstrate that Republicans supported the continued cut. But DeMint and other conservatives led a rebellion, and the bill received a humiliating 20 votes. When McConnell talked his conference into approving a short-term measure instead, it blew up in the House, with conservative members there complaining that McConnell had sold them out.

On Thursday evening, Sen. Harry Reid of Nevada, the majority leader, tried to take up and quickly pass a bill to reauthorize the U.S. Export-Import Bank, an entity established in the 1930s whose authority to exist was to expire at the end of the month. The bill that Reid was turning to had passed the House on Wednesday, 330 to 93. But McConnell held out for amendments requested by DeMint and other conservative members who had denounced the bank as a government boondoggle.

“I used to just talk about the House wing of the Tea Party,” Reid said on the Senate floor on Thursday, “but it is over here now.”

Reid was so frustrated on Thursday that he suggested he might abrogate a gentleman’s agreement with McConnell and sign on to Democratic efforts to change the Senate’s filibuster rule. Republicans now use the filibuster routinely, not just to prevent final votes on legislation but to prevent bills from even reaching the floor for consideration.

Now, Republican hopefuls want the Senate to act more like the house. Dan Liljenquist, a Tea Party-backed Republican challenging Sen. Orrin G. Hatch in Utah’s Primary next month, said Republican leaders in the House, many of them young upstarts themselves, ditched traditional rules of seniority last year and let energetic up-and-comers take on powerful roles. At 42, Rep. Paul D. Ryan of Wisconsin, the House Budget Committee chairman, has become perhaps his party’s most important policy maker.

In the Senate, Liljenquist said, “The leaders most anxious to take on the entitlement system and the entrenched problems the nation faces are being benched by a system that puts them at the bottom rung.”

McConnell, who has been the minority leader since 2007, also finds himself increasingly in the cross hairs of deeply conservative outside groups. Erick Erickson, a blogger, posted a Twitter message on Tuesday night that read: “Dear Mitch McConnell, I hope you heard the Tea Party of Indiana tonight. Heheheh. If not, you will come January.” A conservative radio host, Laura Ingraham, fired off her own Twitter missive: “Is Senate leadership effective under Leader McConnell?”

In some ways, McConnell has always been suspect to conservatives because of his history of supporting federal spending projects and because of his well-known deal-making ability, and recently because he voted for the bank bailout bill that was the match that lighted the Tea Party fire. But he has shown a formidable ability to survive the shifts in the Senate, including a loss of seats under his watch in 2008.

© 2012 The New York Times Company