Failing to raise it may mean a U.S. default on its debt, something Obama stressed in Wednesday's White House meeting that the country can't afford to do, according to Reid.
Obama offered no indication that he'll budge. Noting that such Republican brinkmanship in 2011 led to the first-ever downgrade of the U.S. credit rating, the president said Tuesday he "will not negotiate over Congress' responsibility to pay bills it's already racked up."
Writing the same day in USA Today, Boehner dug in his heels on the issue, saying "there is no way Congress can or should pass such a bill without spending cuts and reforms to deal with the debt and deficit."
Still, that crisis is still a few weeks away. The government shutdown is the one currently affecting hundreds of thousands of furloughed government workers, not to mention millions of others who rely on government programs, visit national parks and have some other type of interaction with affected programs.
One moderate Republican who has backed a clean spending measure, Rep. Michael Grimm of New York, said that "both sides have dug in." Democrats, who he said "won't even have a discussion," put House Republicans in a tight spot where they feel compelled to hold their ground or else "set a bad precedent that the Senate would be somewhat dictating how the House runs."
But if Democrats agreed to listen, Grimm expressed optimism "that we would put a package together and solve the problems at once, so we can get the government funded, stop the shutdown, and also deal with the debt ceiling so we don't have another crisis a week or two away from now."
Pelosi said that scores of Democrats have reluctantly offered to back a plan to fund the entire government at a figure that's been bandied about by Republicans, albeit well below what her party members want. The other option would be to reconcile budgets passed by both chambers earlier this year in a conference committee, as is Washington custom.
But what Democrats won't stand for, Pelosi said, is GOP legislators shuttering the government due to their opposition to Obamacare, which previously passed through Congress and withstood a Supreme Court challenge.
"That's not what our Constitution had in mind: that if you don't like something, you threaten to shut down the government," the California Democrat said. "It's not that kind of system."
A blow to the economy
The shutdown of the government -- the country's largest employer -- isn't happening all at once.
Federal employees who are considered essential will continue working. Those deemed non-essential -- up to 800,000 -- could be furloughed, unsure when they'll be able to work or get paid again.
The shutdown could cost the still-struggling U.S. economy about $1 billion a week in pay lost by furloughed federal workers. And that's only the tip of the iceberg.
While many agencies have reserve funds and contingency plans that would give them some short-term leeway, the economic effect would snowball as the shutdown continued.
The total economic impact is likely to be at least 10 times greater than the simple calculation of lost wages of federal workers, said Brian Kessler, economist with Moody's Analytics. His firm estimates that a three- to four-week shutdown would cost the economy about $55 billion.
And it's already had political ramifications extending beyond the United States. On Wednesday, Obama canceled planned visits next week to Malaysia and the Philippines as part of an Asian swing that will include a summit of the Association of Southeast Asian Nations on Bali. Obama will still attend the ASEAN summit, his office said.