The Senate could be the first to act on the debt ceiling, as Majority Leader Harry Reid, D-Nev., could file a clean bill Tuesday, leading to a procedural vote by Friday, CNN reported. The legislation will reportedly not include spending cuts and changes being requested by Republicans, which means it’s likely a nonstarter.

Action from the Senate though would pressure the House to put forward its own measure to extend the U.S. borrowing authority before the Oct. 17 deadline.

Bloomberg also reported that Senate Democrats could have a test vote by the end of this week on a bill that would give President Barack Obama the authority to increase the $16.7 trillion debt ceiling for about a year.

Without an increase in the debt limit, the U.S. risks a possible default, which could be catastrophic.

Obama has said the debt ceiling is non-negotiable. Recent reports are that the president isn't averse to a short-term agreement just to head off the crisis, but will not make any policy changes.

And earlier Tuesday, House Speaker John Boehner, R-Ohio, has reiterated calls for a discussion with Democrats to work together to come to an agreement.

“By refusing to negotiate, Harry Reid and our president are putting the country on a very dangerous path,” he said.

Adding that no president has ever refused to negotiate over the debt ceiling, the speaker said, “The way to resolve this is to sit down and have a conversation and resolve our differences.”

But Reid countered that Boehner is “still sitting on a bill that could reopen the government” and that Democrats are willing to negotiate on the budget and other issues once the shutdown is lifted.

“First, Republicans must reopen the government and stop threatening a catastrophic default on the nation’s bills,” Reid said. “They must respect the democratic process.”

In the meantime, House Republicans are proceeding to pass piecemeal bills to reopen -- that is, to fund -- selected portions of the government. Democrats have shunned this strategy.

Still, with nine days to go before the debt ceiling is reached, some Republicans are reportedly skeptical of the alarm, according to USA Today. These Republicans say the U.S. Treasury could prioritize interest payments to bondholders, avoiding the default on interest payments and delay others.

“I would dispel the rumor that is going around that you hear on every newscast, that if we don’t raise the debt ceiling, we will default on our debt,” said Sen. Tom Coburn, R-Okla., on CBS “This Morning” on Monday. “We won’t. We’ll continue to pay our interest.”