Updated at 12:15 p.m. ET
On the eighth day of the government shutdown, House Speaker John Boehner, R-Ohio, said that before re-opening the government, Democrats and Republicans should sit down for negotiations without any preconditions.
"The central argument is this: are we going to sit down and have a conversation, or aren't we?" he told reporters. "There's no boundaries here. There's nothing on the table, nothing off the table."
Democrats, meanwhile, insist they've already made a major concession to Republicans by agreeing to the low spending limits that the GOP wanted.
"He can't take yes for an answer," Senate Majority Leader Harry Reid, D-Nev., said on the Senate floor Tuesday, referring to Boehner. "I don't know what else is left to talk about. All we're asking is that government be re-opened."
The government partially shut down on Oct. 1 after Congress failed to pass a spending bill, referred to as a continuing resolution (CR). Republicans have insisted partially dismantling or delaying the Affordable Care Act as part of their budget talks, which Democrats have resisted.
President Obama and Democratic leaders say they are willing to negotiate over spending issues, and potentially some ways to modify the health care law, only after the government is re-opened and Congress raises the debt limit.
Mr. Obama called Boehner around 10:45 a.m. ET on Tuesday "to reiterate that he won't negotiate on a government funding bill or debt limit increase," according to Boehner spokesman Brendan Buck. According to the White House's characterization of the call, "the President telephoned Speaker John Boehner from the Oval Office and repeated what he told him when they met at the White House last week: the President is willing to negotiate with Republicans -- after the threat of government shutdown and default have been removed - over policies that Republicans think would strengthen the country."
Boehner however, said to reporters that the Democrats' refusal to negotiate "is an untenable position."
House Republicans met privately Tuesday morning for about an hour, during which they primarily discussed their strategy to stand firm and wait for Democrats to come to the negotiating table. They also discussed two new bills they'll put forward to respond to the shutdown: One bill would create a negotiating team for the debt limit and other budget issues.
The other bill would ensure "essential" government employees who are still on the clock will get paid on time (Friday through Tuesday is a pay period for many). This should help address the anxiety of federal workers whose bills haven't stopped even though their paychecks have. Under this plan, however, furloughed employees would still have to wait for backpay.
The shutdown is impacting different federal agencies to varying degrees. Nearly 10,000 Veterans Affairs Department employees were furloughed Monday evening. About 3,000 of those employees came from the VA's Office of Information Technology, while 7,000 were from the Veterans Benefits Administration. The furloughs could reverse the progress the VA has made recently in bringing down its disability claims backlog, the agency said in a statement.
"Clear progress for veterans and their families is at risk without immediate action by Congress to make fiscal year 2014 funding available by passing a clean continuing resolution to reopen the government," the statement said.
Meanwhile, in the Defense Department, most civilian employees are returning to work this week. However, there are critical programs and benefits that remain halted, Pentagon leaders told Defense Secretary Chuck Hagel in a meeting Monday. For instance, according to the department, it does not have authority during the shutdown to pay death gratuities for the survivors of servicemembers killed in action - typically a cash payment of $100,000 paid within three days of the death. Additionally, the Pentagon says it is curtailing training for later deploying units, even though funding for that training was already cut under the sequester.
Meanwhile, the Social Security Administration confirmed to CBS News that it's received calls from citizens concerned about the impact the current budget stalemate will have on their Social Security checks. While the shutdown shouldn't impact Social Security checks, benefits could be at risk if Congress fails to raise the debt limit by Oct. 17.
The Social Security Administration crafted a response with the Treasury Department, and field offices are now advising the public that they cannot guarantee full benefit payments if the debt ceiling isn't increased.
CBS News Capitol Hill producer Alicia Budich contributed to this report.