The door for tax increases began to slowly creak open this past week, as Republican leaders and rank-and-file members alike suggested the bipartisan Super Committee tackling the nation's deficit look at revenue -- as a Nov. 23 deadline approaches. 

Republicans are hardly united in, or enthusiastic about, the prospect of tossing in tax hikes to help achieve at least $1.2 trillion in deficit reduction over the next decade. Thirty-three GOP senators fired off a letter on Thursday telling the panel to reform the tax code and lower tax rates in a way that produces "no net tax increase." 

But such an approach would not contribute to the $1.2 trillion deficit-reduction goal. And in the middle of a week chock-full of dire warnings about the direction of the committee and the consequences of failure, House Speaker John Boehner conceded that a final deal could include revenue increases, though "there clearly is a limit." 

Boehner told reporters earlier this week that lawmakers understand the "gravity" of the situation. 

Without a deal in the committee by late November and an affirmative vote in Congress by late December, the legislation that created the committee would trigger deep cuts in defense and entitlements that neither party wants. 

Boehner's comments came after 40 House Republicans and 60 House Democrats wrote a letter urging the group to "go big" and find at least $4 trillion in deficit reduction. In the letter, the lawmakers urged the committee to consider "all options for mandatory and discretionary spending and revenues." 

Lawmakers did not specify which entitlement and other programs they'd be willing to cut, and which taxes they'd be willing to raise. But lawmakers stressed that the committee will have to make tough decisions for the final product to work. 

Rep. Mike Simpson, R-Idaho, said "it's time to cowboy up" and do what is "necessary." 

House Democratic Whip Steny Hoyer, D-Md., said "all spending and revenue must be on the table." 

Republican lawmakers on the committee reportedly are meeting over the weekend to figure out a way forward, and determine how heavily taxes should factor into a compromise package. 

Meanwhile, sources told Fox News that the 100 House lawmakers who pressed the committee earlier this week have joined up with select senators who have worked on taming the nation's debt before to talk about a way to break the stalemate. The so-called "Go Big Coalition" met for an hour Thursday to discuss their options. 

"A lot of people are genuinely fearful that the Super Committee is stalled. The group is simply trying to help find a way to ensure they don't," said one aide to a member who attended the meeting. 

Fox News' Trish Turner contributed to this report.