(CNN) -- Even though polls show House Republicans got much of the blame for the government shutdown triggered by the fight over Obamacare, there are no signs they are giving up on that fight.
With fresh data and the acknowledgment from President Barack Obama that the web portal to enroll in new health care plans isn't working, Speaker John Boehner and other GOP leaders told House Republicans on Wednesday the website's bumpy rollout gives them an opening to seize public attention.
But according to several GOP sources present at the weekly GOP meeting, leaders said they expected the administration would fix those so-called technical "glitches" soon, so House Republicans need to cast the debate more broadly and hone in on the real-world impact that the law is having on Americans.
"At some point the website is going to be working and Obamacare isn't," one senior GOP source who attended the meeting told CNN.
Utah GOP Rep. Jason Chaffetz told CNN the plan going forward was "let's continue the vigorous oversight of Obamacare. It's not just about the website -- it's about a lot of other fundamental flaws."
After meeting with his members, Boehner reinforced that message to reporters.
"When you look at the problems with Obamacare all the focus here lately has been on the website. Clearly there's problems with the website, but I would argue that the problems go much further than that," Boehner said.
Several House Republicans said they plan to demonstrate how the law isn't living up to the goals the President set out when he pushed to create it in 2009.
"You have to start with all the promises that President Obama made to the American people -- it's going to lower costs; if you like what you have, you can keep it; it's going to reduce the deficit," said Rep. Steve Scalise, R-Louisiana.
He argued those promises "are being broken on a daily basis and families are finding out about it and they are demanding that serious questions be asked and we're here to ask those questions."
Asked about his legislative strategy in the aftermath of the fight over defunding or delaying Obamacare as part of the government funding bill, Boehner stressed "the biggest part of Congress' job is to provide proper oversight of the executive branch of government" and noted "when it comes to Obamacare, clearly there's an awful lot that needs to be held accountable."
House Republicans are also renewing their push to delay the Obamacare tax that will be imposed on those who fail to enroll in health care coverage by the deadline at the end of March.
Under the law those who don't sign up will be hit with a penalty on their tax returns of up to 1% of their income.
"With so many unanswered questions and the problems arising around this rollout, it doesn't make any sense to impose this 1% mandate tax on the American people," House Majority Leader Eric Cantor told reporters Wednesday.
During negotiations earlier this month with Obama over extending the nation's debt limit Boehner said Republicans would only be open to a one-year extension if the President agreed to delay this health insurance penalty for one year.
Those negotiations fell apart, but one GOP aide told CNN that continued news coverage about the problems people are finding getting signed up will increase pressure on the White House to agree at least temporarily waive this penalty.
And House Republican aides point out that political pressure from members of the President's own party will only make it tougher for the administration to continue resisting a delay for the mandate tax.
New Hampshire Democratic Sen. Jeanne Shaheen has called for an extension for the enrollment period. Twenty-two House Democrats already voted to delay the mandate on individuals to sign up for health care coverage, and some of those members -- like Georgia Rep. John Barrow -- are beginning to publicly call on the administration to agree to delay that requirement.
In addition to focusing on oversight, House Republicans created a website to collect stories from people who are dealing with problems related to Obamacare.
Aides say the common complaints they want to explore in the coming weeks include rate spikes for young women, and reports about people already insured getting letters informing them they are losing their health care coverage because of Obamacare.
Some House Republicans are quick to stress they don't want to get in another fight that triggers another government shutdown, but believe it's their job to address the problems their constituents are experiencing as Obamacare goes into effect.
"I'm not a part of the 'Hell no' caucus on either the Democrat or Republican side that wants to shut this place down," Florida Republican Rep. Trey Radel told CNN. "What I want to do is be more responsible to the American people and find out ways - if this is the law of the land - how do we make it as efficient as possible for the American people?"