The debt ceiling is not the cause of the current government shutdown, nor will not increasing it benefit anyone. Instead, passing a proper budget would end the shutdown and could change the situation around the multi-trillion dollar debt.
Again, the debt ceiling is something the country will hit in a few weeks, but is not the cause of the shutdown. The leadership's ineptitude and unwillingness to cooperate is the real cause. Unaffected by the shutdown and unaware of the plight of the common man, the leadership is using the shutdown as another move in this game of Chicken with the opposing party. There's the game of Chicken teenagers play with cars where they drive directly at each other until they swerve out of the way, but there's a real, impending sense of danger during that game caused by the very real possibility of death. In this nation-sized game of Chicken, the 535 members of Congress (435 Representatives, 100 Senators) are dueling with no sense of danger.
During this government shutdown, they will continue to receive paychecks. Even if they didn't, they have plenty to survive on between missed paychecks with their 6-figure income and millions in the bank (over 48% of Congress are millionaires). If you were a millionaire and someone was threatening a week's pay of a salary of \$174,000, or only \$3,000, 'holding your ground' would be relatively easy. While much of the nation would be grateful for \$3k, and overjoyed to make that much a week, members of Congress are sitting around idly arguing with each other while hard-working employees are laid off, furloughed, or given IOU's in lieu of real paychecks.
Money continues to influence American politics more than the people and the truth.
This was a PSA about the difference between the debt ceiling and the current government shutdown.