That immigration bill is now struggling for life and attention in the Republican-run House. The bigger worry for many party leaders is the growing rift between business-oriented Republicans and the GOP's more ideological wing. Each accuses the other of bungling the debt ceiling and government shutdown dramas, widely seen as a major Republican embarrassment.
The problems don't end there.
Polls show the GOP nominee trailing in a Virginia governor's race that history says a Republican should win. At the national level, it's hard to recall when Republicans seemed so leaderless. Romney has returned to private life. Potential rising stars have stumbled, as Sen. Marco Rubio of Florida did when he angered conservative activists by pushing the immigration measure through the Senate.
Senate Minority Leader Mitch McConnell is preoccupied with his Kentucky re-election bid, squeezed between a tea party GOP challenger on the right and a well-regarded Democrat on the left. In the House, Speaker John Boehner of Ohio cemented his support among Republican colleagues only by letting them vote heavily against a bipartisan plan to avert an unprecedented default on U.S. obligations.
The legislation, which also reopened the government, passed mostly with Democratic votes. That's hardly the type of victory a Republican speaker hangs on his wall.
Eyeing this troubling landscape, many Republican campaign veterans hope conservative die-hards will narrow their differences with the party's more pragmatic members before next year's elections and the 2016 presidential campaign.
"If we don't find common ground and stand on the same side of the line, we're going to have a very ugly and rough couple of years," said Sara Taylor Fagen, who directed political affairs in President George W. Bush's White House.
Fagen acknowledged newfound tensions between business-oriented Republicans and pro-tea-party Republicans, many of whom refused to raise the debt limit unless Democrats agreed to politically unattainable demands. At risk in the impasse was a government default that would have hammered the economy.
Yet it will be hard to close the rift between the two factions, Fagen said. "I don't think they communicate."
To John Ullyot, a former Senate aide to moderate Republicans, "the big takeaway from this last battle was the true separation of the pro-business, establishment Republicans, and what they see as the rebels who are driving the party over the cliff."
Many GOP donors, Ullyot said, "are starting to hold off on any contributions for the time being, until the party figures out how to deal with these upstart Republicans."
Other Republicans say the situation isn't so dire.
GOP Gov. Chris Christie is coasting toward re-election in Democratic-leaning New Jersey. Many throughout the country are complaining about the troubled sign-up process for Obama's health care law, the Republicans' favorite policy target.
Talk of a party rift "is way overplayed," said Henry Barbour, an activist from Mississippi and co-author of the RNC's post-mortem report on Romney's loss. He said Republicans of all stripes overwhelmingly agree on basic issues, including reduced federal spending, opposition to the health law and "preserving freedom."
But Barbour agreed that top Republicans differ over tactics. He took issue with Texas Sen. Ted Cruz's ultimately doomed drive to block Obama's health care law by taking the federal budget hostage.
Longtime Republican adviser Charlie Black said the battles over the budget and debt ceiling clearly hurt the party. But Black, who advised Sen. John McCain's 2008 presidential campaign, played down the internal divide.
"In most places," he said, "we're 95 percent together." But he added, "there will be a few primaries where there will be some differences."
The specter of Republican primaries disturbs many party loyalists. In the past two Senate elections, tea party-backed insurgents defeated nearly a dozen mainstream Republicans — three of them incumbent senators — in primaries.
Campaign professionals say the results cost Republicans up to five Senate seats they could have won if their nominees were not tea-party candidates.
Now there's talk of an establishment Republican counterrevolution, in which business-oriented candidates would challenge tea party incumbents in next year's primaries.
In Michigan, investment banker Brian Ellis is taking on tea party-backed Rep. Justin Amash, and real estate lawyer David Trott is seeking to oust Rep. Kerry Bentivolio, considered by some Republicans to be more of a gadfly than a reliable tea partyer.
It's not clear whether more than a handful of such challenges will emerge. A bigger question is whether business groups, often supportive of Republicans of all ideological types, will steer more money into bids to oust tea partyers who played down the threat of a federal default.
In interviews, numerous business leaders took wait-and-see stands.
"We have no idea what we're going to have on the table" in the 2014 primaries, U.S. Chamber of Commerce President Tom Donohue told reporters.
Peter A. Wish, a veteran GOP fundraiser from Sarasota, Fla., said the activists he talks with are "pretty much divided" over the fallout from the debt and shutdown debates. Some support Cruz's hard-line stand "regardless of the consequences," Wish said. But another faction, he said, "is totally fed up" with an ideological group "picking fights it can't win."
Tea party groups aren't waiting.
For a third straight election, they hope to oust Republican incumbents they view as too willing to work with Democrats. Those targets could include 35-year veteran Sen. Thad Cochran of Mississippi and Sen. Lindsey Graham of South Carolina, whose resume includes managing the 1998 effort to impeach President Bill Clinton.
Many Republican consultants say the party's internal struggles will continue until a leader emerges as the 2016 presidential nominee. Fagen, however, says she worries that the nominee could be nearly perfect, "but it's not good enough for the ideologues, and they run a third-party candidate."