Is there still an animal in congress who could be called a "deficit hawk"?

It doesn't appear so.  Both the House and Senate GOP tax plans would add more than $1.5 trillion to the budget deficit over ten years and $20 trillion to the national debt.

Reuters:

The Committee for a Responsible Federal Budget, a nonpartisan budget watchdog in Washington, on Friday called a Senate Republican tax plan a "fatally flawed budget buster," likening it to Republican legislation in the House of Representatives that the House tax committee has approved.

Both measures would add $1.5 trillion over 10 years to the annual budget deficit and the $20 trillion national debt, according to congressional tax analysts.

The watchdog group estimated that $900 billion of the projected $1.5 trillion deficit increase would come from business tax cuts. The remainder would come from individual tax cuts, including a cut in the estate tax on inheritance that would help only the richest Americans, it said.

Republicans hold a tenuous 52-48 majority in the Senate. For that reason, if they lose the support of only three senators from their ranks, they cannot pass a tax bill as long as Democrats stay united in their opposition.

Critics of that analysis point out that the lower taxes will likely generate additional revenue:

The Tax Foundation, another nonpartisan group, said the Senate plan would add $1.78 trillion to the deficit over a decade. It estimated that over the same time frame lower taxes would expand the U.S. economy by 3.7 percent, add 925,000 full-time jobs, raise wages by 2.9 percent and generate enough new tax revenue to erase all but $516 billion of the deficit effect.

But it's a stretch to believe in that kind of growth.  The previous ten years have seen less than a 3% rise in GDP.  In the end, cutting taxes and not expecting a massive rise in the deficit and national debt will be a leap of faith.

Some of the usual anti-Trump suspects may be using the projected deficits to squash the bill:

After the Senate plan was released on Thursday, Republican Senator Jeff Flake said in a statement, "I remain concerned over how the current tax reform proposals will grow the already staggering national debt by opting for short-term fixes, while ignoring long-term problems for taxpayers and the economy."

Senator James Lankford said in a statement, "As we work on tax relief, we must also not lose sight of our responsibilities to protect the nation, provide basic government services and confront our federal debt."

Senator Bob Corker, another Republican and a critic of Trump, did not comment after the Senate bill's release but signaled fiscal concerns after the House issued its plan, saying he did not want tax cut legislation that added to the deficit.

Running a temporary deficit to ignite the economy is fine.  We shouldn't be settling for this anemic growth, and tax cuts are by far and away the best way to stimulate economic growth.

But those deficit numbers are scary.  I don't blame some conservatives for balking at adding so much to the deficit – especially since the big reduction in corporate taxes, from 35% to 20%, is going to be immediate and permanent.  Senator Tim Scott says a delay in implementing the corporate tax cut would be beneficial in that respect.  And there are other senators who have suggested a phased in approach to business tax cuts.

These tax bills represent a fundamental change in the Republican theory of governance.  In some ways, the GOP will now accept permanent, high-budget deficits as a necessary evil to promote economic growth.  The only difference between the parties now is that the GOP wants to run those deficits as a result of tax cuts, while Democrats want new government spending to goose the economy.

Not much to chose from if you care about the budget deficit.