Senate Finance Committee Chair Ron Wyden (D-OR) has introduced the No Most Favored Nation Trading with Russia Act. According to the press release, the bill "revokes Russia’s Permanent Normal Trade Relations (PNTR) status and provides the president the power to raise tariffs on a host of Russian products."
The full text of the legislation is here. The press release says "[t]he bill is similar to legislation introduced by Reps. Earl Blumenauer, D-Ore., and Lloyd Doggett, D-Texas in the House." The only big change I see from the Blumenauer/Doggett legislation is the addition of this provision:
SEC. 3. PROCLAMATION OF TARIFFS.
With regard to products of the Russian Federation, the President may proclaim modifications to the rates set forth in the column 2 rate of duty column of the Harmonized Tariff Schedule of the United States if the President determines that the modifications are necessary for the protection of the essential security of the United States.
This provision appears to give the president the authority to raise tariffs on Russian imports above the current column 2 "bad boy" rates if these rates are considered not to be high enough to protect U.S. security.