Assuming you file jointly, then it doesn't matter who pays the tax as long as the IRS gets the money. You can certainly increase your job withholding to cover the taxes from your spouse's self-employment.
Joint filing is almost always better even if your income is uneven. You would file a schedule C for your spouse's SE income, and the net income after expenses is combined with your W-2 job and all your other deductions, credits and dependents on your main form 1040. You don't file the business separately, unless it is an S-corp (which would be unusual, and would require legal and professional tax help to set up correctly.)
