The question, he said, now becomes: Will the Fed taper in March or June? I don't know now, he added, "they're not tapering for a long time now."
"So that's definitely sort of going to be a push-up to markets," Tepper said in a "Squawk Box" interview. "Generally speaking, markets will go up, [because] my basic belief has been when you have large (quantitative easing), markets go up."
(Read more: Stocks no bargain anymore: Leon Cooperman)
Back in May on "Squawk," Tepper said: "There better be a true [Fed] taper or else you might be back into the last half of 1999." At the time, he added, "Guys that are short, they better have a shovel to get themselves out of the grave."
On Tuesday, the founder and president of Appaloosa Management said: "I don't think you're going to get '1999' because I was talking about not tapering in a world where you didn't have politicians who have nearly lost their minds."
Senate Majority Leader Harry Reid and Republican leader Mitch McConnell are said to be getting close to a deal that could end the 15-day government shutdown and shift into February the nation's $16.7 trillion debt ceiling decision ahead of Thursday's deadline.
"It looks like they may have a relatively short-term deal, which is going to not create the kind of confidence you might quite like," Tepper said. "If you get a big, broader budget deal, that would be great and markets could fly."
"Putting aside some of this stuff in D.C., because this is really making it difficult to invest right now," stocks could more toward a more normal 18-20 times multiple some time in the future, he said. "You could have a pretty large increase in stock prices to get to there next year."
Meantime, he continued, "the uncertainty you have [for] three or four months, it may be a little tough for markets to fly up."
Whatever the Senate may pass would then go to the House, where it will likely face Republican resistance. Speaker John Boehner, R-Ohio, will be holding a meeting Tuesday to see where GOP members stand.
(Read more: How a US debt default could hit your finances)
As for the national debt, Tepper said Congress should pass legislation that will ensure that the debt will be paid always. Doing so, he said, "will make things much, much, much more stable, and let the economy not have these issues."
A debt default would be a "huge deal for every single American," he said, adding that most mortgages would go higher.
Tepper's Short Hills, N.J.-based Appaloosa has about $18 billion under management, and he topped Alpha magazine's 12th annual "Rich List"—earning $2.2 billion last year. Appaloosa delivered an after-fee annual return of 30 percent in 2012.
(Read more: Budget impasse 'a wash' for markets: Shiller)
The history of Tepper and "Squawk" dates to September 2010 with an appearance that sparked what was dubbed "The Tepper Rally" after he said the Fed's asset-purchase program virtually guaranteed strength in stocks. Since then, the Dow Jones Industrial Average has gained more than 40 percent and the S&P 500 nearly 50 percent. All 10 sectors of the S&P 500 are up at least 20 percent.