WASHINGTON – From Congress, a pair of Minnesota Republicans send their regrets.

"It's not where we wanted to be, there's no question about that," said Rep. John Kline, a close ally of House Speaker John Boehner. "We had hoped to make more progress toward getting more fairness in Obamacare. We didn't get that."

But Kline, along with Minnesota Republican Erik Paulsen, felt he had no choice but to take the deal that emerged Wednesday from frenzied negotiations between Republican and Democratic leaders in the Senate.

"I think the Republican brand has suffered under what has taken place," said Paulsen, who, like Kline, represents a district that went to President Obama in the 2012 election.

Both took flak from the right and left, particularly from Democrats, who portrayed the two swing-district Republicans as hostages to the GOP's Tea Party wing, which sought to make the government spending resolution a referendum on blocking the new health care law.

The only other Minnesota Republican in Congress, Tea Party stalwart Michele Bachmann, voted against the 11th-hour agreement that ended the government shutdown and averted Thursday's deadline to begin defaulting on the national debt.

Bachmann, however, has long since announced she is not running for re-election. It will be up to Kline and Paulsen — and much of the House GOP leadership — to pick up the pieces of what some Tea Party groups are calling "unconditional surrender."

Both men, who were among 87 Republicans voting for the deal, vowed to fight on in the next round of debt and deficit negotiations that will follow what has been a 16-day impasse. The deal passed the House on a 285-144 vote; no Democrats voted against the deal.

"It's fair to say virtually none of us like this deal," Kline said after coming out of a sobering GOP caucus meeting. "But it's a question of tactics now. Do we move forward? We have upcoming events where we will try to push for the things that we think are important."

Kline faces what could be a spirited rematch with former DFL state Rep. Mike Obermueller, who lost to Kline by 8 percentage points last year. Obermueller released a statement Wednesday accusing Kline of "reckless partisanship" that risked the nation's credit rating. "Just another reminder that Congressman Kline is part of the problem in Washington," Obermueller said.

Kline, in his sixth term, also faces another GOP primary challenge by "grass roots" candidate David Gerson, who faults Kline for his New Year's Eve fiscal cliff vote that averted another financial crisis by letting tax rates rise on the wealthiest taxpayers.

GOP activists in Kline's Second Congressional District south of the Twin Cities say he has little to worry about. "He's considered to be a very reasonable congressman," said Jeff Lorsung, the district's deputy GOP chairman. "Some on the far right would call that squishy. But as it relates to electability, that puts him where people want him to be."

Paulsen, who voted against the fiscal cliff deal last January, has no declared Democratic opponent in the Third District. But party operatives in Washington have been trying to recruit one, pushing out internal polling in recent days purporting to show him vulnerable on the shutdown issue.

Paulsen, however, was able to use the crisis to push for the repeal of a new tax under the health care law that is opposed by Medtronic and other large medical device companies in Minnesota. "I can absolutely tell my constituents that I've been working on finding solutions to break the logjam," he said.

The repeal of the medical device tax, which is unpopular with many Democrats as well as Republicans, was seen for a while as a potential linchpin for compromise. In the end, however, it was dropped.

Still, the issue allowed Paulsen to distance himself from the conservative hard-liners who pressed for what turned out to be a futile shutdown strategy.

With the benefit of hindsight, both Kline and Paulsen acknowledge the flaws in the House GOP strategy of forcing a series of votes tying continued funding of the government to ending or delaying Obama's health care overhaul. "I don't think it was the best way to start," Kline said. "There were some in my conference who were persuaded by, frankly, the junior senator from Texas [Ted Cruz] … so we are where we are."

Both Kline and Paulsen went along with those votes, one of which tied continued government funding to repealing the medical device tax.

Both emphasize they were votes to keep the government open — albeit with conditions the Democrats would not accept.

"I never had any option," said Paulsen, noting that House leaders did not bring a so-called clean funding resolution that would have allowed members to vote to reopen government without conditions.

Amid the angst and recrimination, Democrats and Republicans in Congress pointed to the near-economic cataclysm as an object lesson.

That was particularly true for the two Minnesota Republicans most on the bubble because of the political dynamics of their districts and the growing sense of public frustration on both sides.

"As a Republican, I think it's important for our party to understand that we need to be for positive solutions, and not just always saying no," Paulsen said.

Said Kline: "This is a time for all of us for reflection."

Follow Kevin Diaz on Twitter @StribDiaz.