The negotiations between GOP leaders and President Barack Obama are "pretty encouraging" and could lead to a breakthrough to temporarily raise the debt ceiling and reopen the government, Rep. Kevin Brady, R-Texas, chairman of the Joint Economic Committee, told CNBC Friday. He also said that trying to repeal Obamacare as part of the budget talks was a "bridge too far."
A delegation of 20 House Republicans met with the president on Thursday—sparking hopes that an agreement may be near.
"I don't know the timetable. But the negotiations are pretty encouraging," Brady said in a "Squawk Box" interview—advocating the approach of buying "six weeks to come together with a solution to the debt ceiling."
He added, "Let's put the Budget Committee back together between the Senate and House, and find a resolution to our budget figures for the next year."
"And let's start to talk on how to reopen the government and what that final solution is on the debt ceiling," Brady said. "This could be a breakthrough."
Meanwhile, President Obama is scheduled to meet Friday with Senate Republicans. Ahead of that meeting, Sen. Tom Coburn, R-Okla., a banking committee member, told CNBC that he questions why the U.S. even has a debt limit. "If you always raise the debt limit, there's not a limit," he said.
"The debt limit is the one thing that will force the reality on Congress that we have to deal with our unfunded liabilities," he said on "Squawk Box" Friday. "We have a debt limit out there and it's the international financial markets. When they don't see us addressing the very real problems that are causing us to continue to have deficits then they're going to price our securities in such as way we can't afford them."
The signs of thawing in Washington came as a new poll showed just how frustrated the American public is with the politics surrounding the 11-day federal closure and next week's deadline to increase the nation's borrowing limit.
(Read more: Hopes of US deal rise as shutdown enters another day)
According to a NBC News/Wall Street Journal poll, 60 percent of the respondents would vote to defeat and replace every single member of Congress if they could. Only 35 percent said they would not, while 5 percent said they were unsure.
(Read more: Dow gains 320 pointson hopes of DC compromise)
"We should be bracing for mixed messages. It's pretty hard to figure out the second order effects of the shutdown," Thomas Lee, chief U.S. equity strategist at JPMorgan, told "Squawk Box" Friday. "The upshot is ... it does give us somewhat of an insurance policy when it comes to monetary policy. I think the markets are going to feel like, well this is going to give an excuse for easier money for a bit longer."
The Federal Reserve is scheduled to meet later this month and in December. Wall Street will be looking to those meetings for signs that the central bank might start to taper its $85-billion-a-month bond-buying program. Policymakers surprised investors by declining to scale back asset purchases at their September meeting.
"There's [also] still a pent-up demand story," he continued. "A lot of these are temporary disruptions. And I think that's why the market's going to show some relief when we get a resolution."
Lee stood by his prediction of 1,775 on the S&P 500 Index by year-end. "It may not start until November, but we are maintaining our target," he said.