(Brendan Smialowski/GETTY IMAGES)

House Majority Leader Eric Cantor (R-Va.) penned a lengthy memo to his caucus, urging members to hold the line in opposition to tax increases as part of any debt-reduction package.

“Over the next several months, there will be tremendous pressure on Congress to prove that S&P’s analysis of the inability of the political parties to bridge our differences is wrong,” Cantor wrote. “In short, there will be pressure to compromise on tax increases. We will be told that there is no other way forward. I respectfully disagree.”

Cantor argued that, based on the deficit savings identified by House Republicans in their fiscal year 2012 budget blueprint — as well as by the bipartisan working group led this spring by Vice President Biden — congressional leaders can work out a deal that reduces the debt by at least $1.2 trillion without raising taxes.

“Our country currently faces two very serious crises — debt and jobs,” Cantor wrote. “These two crises are not mutually exclusive, but they are equally dangerous. That is why it is absolutely critical that as policies are developed to overcome each, we consider their impact upon each other. Anything less would be negligent.”

As the Dow plunged 635 points Monday, House Speaker John A. Boehner (R-Ohio) said that the dive by the markets was a reminder that “this challenge is ultimately about jobs and our economy” – and that tax increases should remain off the table.

“Providing economic certainty and creating an environment in which businesses can invest and jobs can flourish must remain our number-one focus,” Boehner said in a statement. “That’s why raising taxes is simply the wrong approach.”

In a statement following President Obama’s first remarks since the S&P decision, House Minority Leader Nancy Pelosi (D-Calif.) said that Democrats “will continue to hold true to our values of protecting and strengthening Medicare, Medicaid, and Social Security” as the joint committee carries on its work addressing deficit reduction.

“In the long term, we agree that we must seek a balanced approach that will reduce the deficit, create jobs to grow our economy, and strengthen the middle class,” Pelosi said.

House Minority Whip Steny Hoyer (D-Md.) said that, while there were “clearly some legitimate concerns” with the rating agency’s analysis, “I share the President’s view that the greatest barrier to restoring our fiscal health is not economic — it is political.”

Like Pelosi, Hoyer advocated for a “balanced” approach to resolving the debt problem, involving both spending cuts and tax increases.

Meanwhile, the Senate Banking Committee is reportedly preparing to probe S&P’s decision, Reuters reported Monday afternoon. An aide to the committee did not immediately respond to a request for comment.

In a statement earlier Monday, Senate Banking Committee Chairman Tim Johnson (D-S.D.) sharply criticized Standard & Poor’s, saying he was “deeply disappointed in S&P’s decision to enter into the game of political punditry” by downgrading the country’s credit rating from AAA to AA+.

“As the financial markets stumble, investors continue to regard Treasury debt as a safe haven in times of economic uncertainty,” Johnson said. “This irresponsible move by S&P may, however, have spillover effects that tax the American people by increasing interest rates on home loans, credit cards, and car loans, and by increasing the cost of finance for some state and local governments.”