Connolly said more generally that the U.S. needs to shift to wind and solar as sources of energy in addition to raising taxes on oil companies, and said these are the only ways to end U.S. dependence on foreign oil.

Rep. Marcy Kaptur (D-Ohio) offered another proposal: end the wars in the Middle East and use the money the U.S. spends on those wars to develop domestic energy resources.

"Why don't we invest those trillions and trillions of dollars we are spending in the Middle East to import that oil ... here in our country?" she asked. "We literally could rebuild energy production capacity and much more from one end of our country to the other, and create millions of jobs doing it."

On Thursday, Republicans are expected to consider a bill to restart offshore lease sales, H.R. 1230, and possibly a bill requiring the Department of the Interior to act within 30 days on Gulf of Mexico drilling permit applications.

Despite comments from Connolly and Kaptur, several Democrats have also been vocal about the need to expand offshore drilling, in particular Democrats from Gulf states.

Shortly after noon, Rep. David Cicilline (D-R.I.) said he was sending a letter to House Speaker John BoehnerJohn Andrew BoehnerHillicon Valley: Trump hits China with massive tech tariffs | Facebook meets with GOP leaders over bias allegations | Judge sends Manafort to jail ahead of trial | AT&T completes Time Warner purchase Facebook execs to meet with GOP leaders over concerns about anti-conservative bias Boehner: Federal government should not interfere in recreational marijuana decisions MORE (R-Ohio) asking him to call up legislation that would allow the government to tap oil in the Strategic Petroleum Reserve, and prevent what he called "price gouging" by oil companies. However, these ideas are also expected to be ignored by House Republicans.

-- This story was updated at 12:35 p.m.